Internal problem ID [12860]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 10. Applications of Systems of Equations. Exercises 10.2 page 432
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve([diff(x(t),t)=-x(t)-2*y(t),diff(y(t),t)=5*x(t)+1*y(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 {3 c_{1} \cos \left (3 t \right )}{2}+\frac {3 c_{2} \sin \left (3 t \right )}{2}-\frac {c_{1} \sin \left (3 t \right )}{2}-\frac {c_{2} \cos \left (3 t \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 54
DSolve[{x'[t]==-x[t]-2*y[t],y'[t]==5*x[t]+1*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (3 t)-\frac {1}{3} (c_1+2 c_2) \sin (3 t) \\ y(t)\to c_2 \cos (3 t)+\frac {1}{3} (5 c_1+c_2) \sin (3 t) \\ \end{align*}