Internal problem ID [11933]
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: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+t -{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+y \left (t \right )-t +2 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 42
dsolve([2*diff(x(t),t)+diff(y(t),t)-3*x(t)-y(t)=t,diff(x(t),t)+diff(y(t),t)-4*x(t)-y(t)=exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= t -1-\frac {{\mathrm e}^{t}}{2}+c_{2} {\mathrm e}^{-t} \\ y \left (t \right ) &= -\frac {5 c_{2} {\mathrm e}^{-t}}{2}-4 t +1+c_{1} {\mathrm e}^{t}-\frac {{\mathrm e}^{t} t}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.665 (sec). Leaf size: 72
DSolve[{2*x'[t]+y'[t]-3*x[t]-y[t]==t,x'[t]+y'[t]+4*x[t]-y[t]==Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {t}{7}+\frac {e^t}{6}+c_1 e^{7 t}-\frac {1}{49} \\ y(t)\to -\frac {4 t}{7}-\frac {11}{6} c_1 e^{7 t}+\frac {1}{36} e^t (6 t-11+66 c_1+36 c_2)-\frac {39}{49} \\ \end{align*}