Internal problem ID [11931]
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: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+2 \,{\mathrm e}^{t}\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(x(t),t)+diff(y(t),t)-x(t)-2*y(t)=2*exp(t),diff(x(t),t)+diff(y(t),t)-3*x(t)-4*y(t)=exp(2*t)],singsol=all)
\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{t} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{2 t}}{2}-2 \,{\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 25
DSolve[{x'[t]+y'[t]-x[t]-2*y[t]==2*Exp[t],x'[t]+y'[t]-3*x[t]-4*y[t]==Exp[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 e^t \\ y(t)\to -\frac {1}{2} e^t \left (e^t+4\right ) \\ \end{align*}