#4480 Maxima differential equations

[Allan James Payne]

Problems with diff equations as follows:
Problem 1
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: ode2(eq, y,x);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title, "Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1(sol) 'diff(y(x),x,1)=y(x)-x^2+1
"not a proper differential equation"(sol) false ysol(x):=rhs(sol) false
Problem 2
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title, "Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

desolve(<eqn>,<depvar>): dependent variable <depvar> cannot be a mapatom, found: y</depvar></depvar></eqn>

-- an error. To debug this try: debugmode(true);

[Jaime E. Villate]

This is not a bug but a wrong use of program ode2.
You should do something as the following:

(%i1) eq: 'diff(y, x) = y - x^2 + 1;
                                dy        2
(%o1)                           ── = y - x  + 1
                                dx
(%i2) gsol: ode2(eq, y,x);
                           2              - x     - x         x
(%o2)           y = (- (- x  - 2 x - 2) %e    - %e    + %c) %e
(%i3) psol: ic1(gsol,x=0,y=1);
                                    2
(%o3)                          y = x  + 2 x + 1
(%i4) ysol(x) := rhs(psol);
(%o4)                        ysol(x) := rhs(psol)
(%i5) plot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title, "Solution of the Differential Equation"]);

Notice that ode2 expects and equation with variables such as x and y, and not x and y(x). The solution given by ode2 is a general solution, which cannot be plotted because it has an unknown integration constant %c. You can plot a particular solution (psol above), which can be obtained by giving initial conditions with the program ic1. Please read the documentation for ode2.

[Jaime E. Villate]

And in problem 2, desolve should be used as:

desolve(eq, y(x));

And not as you did. Both ode2 and desolve give you error messages in the examples you showed. You should not proceed to try to see a plot after such error messages. Also, the result of desolve will be a general solution, with an unknown variable, which cannot be plotted. To get a particular solution (which can be plotted) you have to use atvalue, in the case of desolve.

[Allan James Payne]

Query
(%i4) eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y(x));
atvalue(y(x),x=0,1);
wxplot2d(y, [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title, "Solution
of the Differential Equation"]);
wxplot2d(y(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

(sol) y(x)=(y(0)-1)%e^x+x^2+2x+1

(%o3) 1

plot2d: unknown function: y

-- an error. To debug this try: debugmode(true);

On Fri, Jan 31, 2025 at 7:04 PM Stavros Macrakis macrakis@users.sourceforge.net wrote:

• status: open --> not-a-bug

---

[bugs:#4480] https://sourceforge.net/p/maxima/bugs/4480/ Maxima
differential equations

Status: not-a-bug
Group: None
Labels: diff eqs general
Created: Fri Jan 31, 2025 05:35 PM UTC by Allan James Payne
Last Updated: Fri Jan 31, 2025 06:36 PM UTC
Owner: nobody

Problems with diff equations as follows:
Problem 1
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: ode2(eq, y,x);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1(sol) 'diff(y(x),x,1)=y(x)-x^2+1
"not a proper differential equation"(sol) false ysol(x):=rhs(sol) false
Problem 2
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

desolve(<eqn>,<depvar>): dependent variable <depvar> cannot be a mapatom,
found: y</depvar></depvar></eqn>

-- an error. To debug this try: debugmode(true);

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[Raymond Toy]

I don't work with desolve very much, but I think you did things in the wrong order. And you misunderstand what desolve returns.

This works a bit better in getting a solution:

(%i10) atvalue(y(x),x=0,1);
(%o10)                                 1
(%i11) sol: desolve(eq, y(x));
                                      2
(%o11)                        y(x) = x  + 2 x + 1
(%i12) plot2d(rhs(sol), [x,-5,5]);

In any case, bug reports are not for help. Please ask on the maxima mailing list for help.

[Jaime E. Villate]

On 03/02/25 16:50, Allan James Payne wrote:

Query
(%i4) eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y(x));
atvalue(y(x),x=0,1);
wxplot2d(y, [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title, "Solution
of the Differential Equation"]);
wxplot2d(y(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

(sol) y(x)=(y(0)-1)%e^x+x^2+2x+1

(%o3) 1

plot2d: unknown function: y

-- an error. To debug this try: debugmode(true);

Hello,

I don't know how you are using Maxima, but what we are all used to doing
is to enter a command, look at its output to see if it works correctly
and gives a result that we expected and only then continue to do the
following part. In your case, I get the following:

(%i1) eq: 'diff(y(x), x) = y(x) - x^2 + 1;
                         d                   2
(%o1)                    ── (y(x)) = y(x) - x  + 1
                         dx
(%i2) sol: desolve(eq, y(x));
                                       x    2
(%o2)              y(x) = (y(0) - 1) %e  + x  + 2 x + 1
(%i3) atvalue(y(x),x=0,1);
(%o3)                                1

%o2 shows an equation, not the definition of a function. And %i3 didn't
produce any function either (that means that command was not used as it
should be); the result "1" is unexpected. You cannot try to plot y(x)
because at this point you have not defined any function y(x). You could
try to plot the right-hand side of %o2, an expression, but plot2d will
complain that the value of y(0) is unknown (that's what atvalue should
have defined if it had been correct and used before desolve).

However, you could still proceed if you substitute a value for y(0) and
then do the plot:

(%i4) plot2d (subst(y(0)=1,rhs(%o2)), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"]);

The good thing is that you have now discovered the right place where to
ask for help :)

Regards,

Jaime

[Allan James Payne]

Hi Jamie
Thanks for your comments. I make up a cell as a set of commands which I
develop as I go along.
I had expected the desolve to give a general solution and the atvalue after
the desolve to make it a particular solution so that I can graph the
function. I made a simple test to show the problem. I understand the fact
that the plot should have a particular solution.
I think that there is a problem witth atvalue which I would have thought
provided a value for y(0). and there is a bug.
Thank you for your help.
Rgds Allan Payne

On Mon, Feb 3, 2025 at 6:31 PM Jaime E. Villate villate@users.sourceforge.net wrote:

On 03/02/25 16:50, Allan James Payne wrote:

Query
(%i4) eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y(x));
atvalue(y(x),x=0,1);
wxplot2d(y, [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title, "Solution
of the Differential Equation"]);
wxplot2d(y(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

(sol) y(x)=(y(0)-1)%e^x+x^2+2x+1

(%o3) 1

plot2d: unknown function: y

-- an error. To debug this try: debugmode(true);

Hello,

I don't know how you are using Maxima, but what we are all used to doing
is to enter a command, look at its output to see if it works correctly
and gives a result that we expected and only then continue to do the
following part. In your case, I get the following:

(%i1) eq: 'diff(y(x), x) = y(x) - x^2 + 1;
d 2
(%o1) ── (y(x)) = y(x) - x + 1
dx
(%i2) sol: desolve(eq, y(x));
x 2
(%o2) y(x) = (y(0) - 1) %e + x + 2 x + 1
(%i3) atvalue(y(x),x=0,1);
(%o3) 1

%o2 shows an equation, not the definition of a function. And %i3 didn't
produce any function either (that means that command was not used as it
should be); the result "1" is unexpected. You cannot try to plot y(x)
because at this point you have not defined any function y(x). You could
try to plot the right-hand side of %o2, an expression, but plot2d will
complain that the value of y(0) is unknown (that's what atvalue should
have defined if it had been correct and used before desolve).

However, you could still proceed if you substitute a value for y(0) and
then do the plot:

(%i4) plot2d (subst(y(0)=1,rhs(%o2)), [x, -5, 5], [ylabel, "y(x)"], [xlabel,
"x"]);

The good thing is that you have now discovered the right place where to
ask for help :)

Regards,

Jaime

[bugs:#4480] https://sourceforge.net/p/maxima/bugs/4480/ Maxima
differential equations

Status: not-a-bug
Group: None
Labels: diff eqs general
Created: Fri Jan 31, 2025 05:35 PM UTC by Allan James Payne
Last Updated: Mon Feb 03, 2025 05:19 PM UTC
Owner: nobody

Problems with diff equations as follows:
Problem 1
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: ode2(eq, y,x);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1(sol) 'diff(y(x),x,1)=y(x)-x^2+1
"not a proper differential equation"(sol) false ysol(x):=rhs(sol) false
Problem 2
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

desolve(<eqn>,<depvar>): dependent variable <depvar> cannot be a mapatom,
found: y</depvar></depvar></eqn>

-- an error. To debug this try: debugmode(true);

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https://sourceforge.net/p/maxima/bugs/4480/

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[Jaime E. Villate]

On 03/02/25 20:33, Allan James Payne wrote:

I think that there is a problem witth atvalue which I would have thought
provided a value for y(0). and there is a bug.

No that is not a bug. It is well documented that atvalue must be used
before desolve, because desolve uses the Laplace transform, so the
initial condition must be given before desolve calls "laplace".

That is different from the behavior of ode2 and ic1, because in order
for ic1 to evaluate the value of the integration constant, ode2 must
first do its job giving a result with an integration constant %c.

You should take a look at the examples in:

https://maxima.sourceforge.io/docs/manual/maxima_111.html

Finally, I was wrong when I said that "you have found the right place to
ask for help". You should be asking this kind of questions in the list
maxima-discuss (see: https:///maxima.sourceforge.io/maximalist.html) and
not here.

Even the experts who have worked with Maxima for several decades usually
write in that list when they think they have found a bug, before opening
a bug report.

Regards,

Jaime

[Allan James Payne]

Hi Jamie
Thanks for your email. I will go back to sleep. I am sorry to have caused
any trouble .
Rgds Allan Payne

On Mon, Feb 3, 2025 at 8:47 PM Jaime E. Villate villate@users.sourceforge.net wrote:

On 03/02/25 20:33, Allan James Payne wrote:

I think that there is a problem witth atvalue which I would have thought
provided a value for y(0). and there is a bug.

No that is not a bug. It is well documented that atvalue must be used
before desolve, because desolve uses the Laplace transform, so the
initial condition must be given before desolve calls "laplace".

That is different from the behavior of ode2 and ic1, because in order
for ic1 to evaluate the value of the integration constant, ode2 must
first do its job giving a result with an integration constant %c.

You should take a look at the examples in:

https://maxima.sourceforge.io/docs/manual/maxima_111.html

Finally, I was wrong when I said that "you have found the right place to
ask for help". You should be asking this kind of questions in the list
maxima-discuss (see: https:///maxima.sourceforge.io/maximalist.html
https://sourceforge.net/maxima.sourceforge.io/maximalist.html) and
not here.

Even the experts who have worked with Maxima for several decades usually
write in that list when they think they have found a bug, before opening
a bug report.

Regards,

Jaime

[bugs:#4480] https://sourceforge.net/p/maxima/bugs/4480/ Maxima
differential equations

Status: not-a-bug
Group: None
Labels: diff eqs general
Created: Fri Jan 31, 2025 05:35 PM UTC by Allan James Payne
Last Updated: Mon Feb 03, 2025 05:19 PM UTC
Owner: nobody

Problems with diff equations as follows:
Problem 1
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: ode2(eq, y,x);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1(sol) 'diff(y(x),x,1)=y(x)-x^2+1
"not a proper differential equation"(sol) false ysol(x):=rhs(sol) false
Problem 2
eq: 'diff(y(x), x) = y(x) - x^2 + 1;
sol: desolve(eq, y);
ysol(x) := rhs(sol);
wxplot2d(ysol(x), [x, -5, 5], [ylabel, "y(x)"], [xlabel, "x"], [title,
"Solution of the Differential Equation"]);
(eq) 'diff(y(x),x,1)=y(x)-x^2+1

desolve(<eqn>,<depvar>): dependent variable <depvar> cannot be a mapatom,
found: y</depvar></depvar></eqn>

-- an error. To debug this try: debugmode(true);

Sent from sourceforge.net because you indicated interest in
https://sourceforge.net/p/maxima/bugs/4480/

To unsubscribe from further messages, please visit
https://sourceforge.net/auth/subscriptions/

[Raymond Toy]

You have not caused trouble. If you have further questions, please use the mailing list. There are lots more people reading that than bug reports and you'll get more help there. We welcome new users to join the list and ask questions!

[Jaime E. Villate]

On 03/02/25 21:39, Raymond Toy wrote:

You have not caused trouble. If you have further questions, please use the mailing list. There are lots more people reading that than bug reports and you'll get more help there. We welcome new users to join the list and ask questions!

Exactly! I was actually happy to talk about solving differential
equations using ode2 and desolve. I also run into similar problems as
you did when I started using Maxima 30 years ago. Then I taught a course
on differential equations using Maxima for several years, but I haven't
had the chance to teach that course again in the last few years, so any
opportunity to talk about the subject is always welcome.

Jaime