Internal problem ID [15507]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 20. The method of elimination.
Exercises page 212
Problem number: 776.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-9 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-9*y(t),diff(y(t),t)=x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \\ y \left (t \right ) &= -\frac {c_{1} \cos \left (3 t \right )}{3}+\frac {c_{2} \sin \left (3 t \right )}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 42
DSolve[{x'[t]==-9*y[t],y'[t]==x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (3 t)-3 c_2 \sin (3 t) \\ y(t)\to c_2 \cos (3 t)+\frac {1}{3} c_1 \sin (3 t) \\ \end{align*}