Internal problem ID [9465]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1886.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\relax (t )+a y \relax (t )&=0\\ y^{\prime \prime }\relax (t )-a^{2} y \relax (t )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 50
dsolve({diff(x(t),t,t)+a*y(t)=0,diff(y(t),t,t)-a^2*y(t)=0},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = -\frac {-t c_{1} a +c_{3} {\mathrm e}^{a t}+c_{4} {\mathrm e}^{-a t}-c_{2} a}{a} \] \[ y \relax (t ) = c_{3} {\mathrm e}^{a t}+c_{4} {\mathrm e}^{-a t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 65
DSolve[{x''[t]+a*y[t]==0,y''[t]-a^2*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {a (a (c_2 t+c_1)-c_3 \cosh (a t)+c_4 t+c_3)-c_4 \sinh (a t)}{a^2} \\ y(t)\to c_3 \cosh (a t)+\frac {c_4 \sinh (a t)}{a} \\ \end{align*}