Internal problem ID [11929]
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: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )-2 t\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=t^{2}+3 x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve([diff(x(t),t)+diff(y(t),t)-x(t)=-2*t,diff(x(t),t)+diff(y(t),t)-3*x(t)-y(t)=t^2],singsol=all)
\begin{align*} x \left (t \right ) &= -2+{\mathrm e}^{-t} c_{1} \\ y \left (t \right ) &= -t^{2}+4-2 \,{\mathrm e}^{-t} c_{1} -2 t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 42
DSolve[{x'[t]+y'[t]-x[t]==-2*t,x'[t]+y'[t]-3*x[t]-y[t]==t^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -2-\frac {1}{4} c_1 e^{-t} \\ y(t)\to -t^2-2 t+\frac {c_1 e^{-t}}{2}+4 \\ \end{align*}