> From: Mahery Raharinjatovo
> I have a question
> Can maxima solve this equation
> 'diff(x,t,2)+k/m*x=0 ?
>
> I try with ode2
>
> (%i1) ode2('diff(x,t,2)+k/m*x=0, x, t);
> but maxima return this
> "Is k*m positive, negative, or zero?"
The solution depends on the sign of k*m. You need to
provide this additional information to maxima.
If k>0 and m>0 then you have the first case, a simple harmonic
oscillator.
(%i1) ode2('diff(x,t,2)+k/m*x=0, x, t);
Is k m positive, negative, or zero?
pos;
sqrt(k) t sqrt(k) t
(%o1) x = %k1 sin(---------) + %k2 cos(---------)
sqrt(m) sqrt(m)
(%i2) ode2('diff(x,t,2)+k/m*x=0, x, t);
Is k m positive, negative, or zero?
neg;
%i sqrt(k) t %i sqrt(k) t
------------ - ------------
sqrt(m) sqrt(m)
(%o2) x = %k1 %e + %k2 %e
(%i3) ode2('diff(x,t,2)+k/m*x=0, x, t);
Is k m positive, negative, or zero?
zero;
(%o3) x = %k2 t + %k1
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