Re: [Maxima-discuss] How do I make ode2 prefer complex solutions?

[Stavros M. <mac...@gm...>]

For the last question, try scanmap('factor,f2).


On Sat, Jul 8, 2023, 15:06 Eduardo Ochs <edu...@gm...> wrote:

> Hi all,
>
> I am trying to translate to Maxima some exercises that I gave to my
> students. In this code
>
>   edo     :  y_xx + 4*y_x + 29*y = 0;
>   edo2    :  subst([y_xx='diff(y,x,2), y_x='diff(y,x)     ], edo);
>   edo2(f) := subst([y_xx= diff(f,x,2), y_x= diff(f,x), y=f], edo);
>   sols    :     ode2(edo2,y,x);
>   sol0    : rhs(ode2(edo2,y,x));
>   f3      : subst([%k1=0, %k2=1], sol0);
>   f4      : subst([%k1=1, %k2=0], sol0);
>   f1      : expand(exponentialize(f3 + %i*f4));
>   f2      : expand(exponentialize(f3 - %i*f4));
>   expand(edo2(f1));
>   expand(edo2(f2));
>   expand(edo2(f3));
>   expand(edo2(f4));
>   display2d:false$
>   sol0;
>   f1;
>   f2;
>   f3;
>   f4;
>
> ode2 prefers to return the basic real solutions of the ODE "edo" - see
> sol0, f3 and f4 here...
>
>   (%i15) sol0;
>   (%o15) %e^-(2*x)*(%k1*sin(5*x)+%k2*cos(5*x))
>   (%i16) f1;
>   (%o16) %e^(5*%i*x-2*x)
>   (%i17) f2;
>   (%o17) %e^((-5*%i*x)-2*x)
>   (%i18) f3;
>   (%o18) %e^-(2*x)*cos(5*x)
>   (%i19) f4;
>   (%o19) %e^-(2*x)*sin(5*x)
>   (%i20)
>
> ...and I had to do some (simple) juggling to obtain the basic complex
> solutions, that are f1 and f2.
>
> Is there a flag that makes ode2 prefer the complex solutions instead
> of the real ones? And, btw, how do I make Maxima move the x in
>
>   %e^((-5*%i*x)-2*x)
>
> outside, and transform that expression into this?
>
>   %e^((-2-5*%i)*x)
>
> Thanks in advance! =)
>   Eduardo Ochs
>   http://anggtwu.net/eev-maxima.html
>
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