[Maxima-discuss] ode2 output with separable ODEs

[Aleksas D. <ale...@gm...>]

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