Internal problem ID [11932]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 7, Systems of linear differential equations. Section 7.1. Exercises page
277
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right )-{\mathrm e}^{t}+{\mathrm e}^{-t}\\ y^{\prime }\left (t \right )&=-5 x \left (t \right )-3 y \left (t \right )+2 \,{\mathrm e}^{t}-{\mathrm e}^{-t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 48
dsolve([2*diff(x(t),t)+diff(y(t),t)-x(t)-y(t)=exp(-t),diff(x(t),t)+diff(y(t),t)+2*x(t)+y(t)=exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ y \left (t \right ) &= \frac {c_{1} \cos \left (t \right )}{2}-\frac {3 c_{2} \cos \left (t \right )}{2}-\frac {3 c_{1} \sin \left (t \right )}{2}-\frac {c_{2} \sin \left (t \right )}{2}+\frac {{\mathrm e}^{t}}{2}-\frac {{\mathrm e}^{-t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 60
DSolve[{2*x'[t]+y'[t]-x[t]-y[t]==Exp[-t],x'[t]+y'[t]+2*x[t]+y[t]==Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (t)+(3 c_1+2 c_2) \sin (t) \\ y(t)\to \frac {1}{2} \left (-e^{-t}+e^t+2 c_2 \cos (t)-2 (5 c_1+3 c_2) \sin (t)\right ) \\ \end{align*}