From: Ralf S. <gt...@gm...> - 2015-02-07 07:23:03
|
Hello, is there a specific reason why maxima won't apply solve to equations resulting from some ode2 calls? (%i1) ode2('diff(y,x)=y^2, y, x); 1 (%o1) - - = x + %c y (%i2) ode2('diff(y,x)=y^2+1, y, x); (%o2) atan(y) = x + %c This looks inconsistent with (%i3) ode2('diff(y,x)=y, y, x); x (%o3) y = %c %e Regards, |
From: Aleksas D. <ale...@gm...> - 2015-02-08 14:30:10
|
On 07-02-2015 07:22, Ralf Stephan wrote: Hello, is there a specific reason why maxima won't apply solve to equations resulting from some ode2 calls? (%i1) ode2('diff(y,x)=y^2, y, x); 1 (%o1) - - = x + %c y (%i2) ode2('diff(y,x)=y^2+1, y, x); (%o2) atan(y) = x + %c This looks inconsistent with (%i3) ode2('diff(y,x)=y, y, x); x (%o3) y = %c %e Regards, ---------------------------------------------------------- (%i1) ode2('diff(y,x)=y^2, y, x); (%o1) -1/y=x+%c (%i2) method; (%o2) separable (%i3) ode2('diff(y,x)=y^2+1, y, x); (%o3) atan(y)=x+%c (%i4) method; (%o4) separable (%i5) ode2('diff(y,x)=y, y, x); (%o5) y=%c*%e^x (%i6) method; (%o6) linear First two equations maxima solve as separable. In this case solution is implicit: (%i7) ode2('diff(y,x)=f(x)*g(y),y,x); (%o7) integrate(1/g(y),y)=integrate(f(x),x)+%c (%i8) method; (%o8) separable Third equation maxima solve as linear. In this case solution is exact: (%i9) ode2('diff(y,x)+p(x)*y=f(x), y, x); (%o9) y=%e^-integrate(p(x),x)*(integrate(f(x)*%e^integrate(p(x),x),x)+%c) (%i10) method; (%o10) linear best regards, Aleksas Domarkas |
From: Ralf S. <gt...@gm...> - 2015-02-08 14:58:08
|
On Sun Feb 08 2015 at 3:31:33 PM Aleksas Domarkas <ale...@gm...> wrote: > > First two equations maxima solve as separable. > In this case solution is implicit: > (%i8) method; > (%o8) separable > I do not deny that the general solution must be of this form. You also convinced me at least that the output is consistent. But in the given cases it would be correct to solve for y(x), and we should do so because it would be convenient to the user. Regards, |
From: Richard F. <fa...@be...> - 2015-02-08 17:00:43
|
On 2/8/2015 6:30 AM, Aleksas Domarkas wrote: > > On 07-02-2015 07:22, Ralf Stephan wrote: > > Hello, > is there a specific reason why maxima won't apply solve to equations > resulting from some ode2 calls? > Some times the results in text books are given in implicit form, also. Maybe because it is sometimes simpler. |
From: Jaime V. <vi...@fe...> - 2015-02-07 09:41:04
|
On 07-02-2015 07:22, Ralf Stephan wrote: > is there a specific reason why maxima won't apply solve to equations > resulting from some ode2 calls? Hi, ode2 does not apply solve to any equation; you would have to do that yourself. The fact that in some cases ode2 gives a solution of the form y=f(x,%c) is, I believe, purely accidental and not because it is trying to put the result in that form. Regards, Jaime |