Internal problem ID [11930]
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: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=-x \left (t \right )+{\mathrm e}^{3 t} \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 37
dsolve([diff(x(t),t)+diff(y(t),t)-x(t)-3*y(t)=exp(t),diff(x(t),t)+diff(y(t),t)+x(t)=exp(3*t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {{\mathrm e}^{t}}{4}+c_{1} {\mathrm e}^{-3 t} \\ y \left (t \right ) &= \frac {{\mathrm e}^{3 t}}{3}-\frac {{\mathrm e}^{t}}{2}-\frac {2 c_{1} {\mathrm e}^{-3 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 55
DSolve[{x'[t]+y'[t]-x[t]-3*y[t]==Exp[t],x'[t]+y'[t]+x[t]==Exp[3*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {e^t}{4}+\frac {3}{16} c_1 e^{-3 t} \\ y(t)\to -\frac {e^t}{2}+\frac {e^{3 t}}{3}-\frac {1}{8} c_1 e^{-3 t} \\ \end{align*}