Internal problem ID [11940]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-t^{2}+x \left (t \right )+y \left (t \right )+6 t\\ y^{\prime }\left (t \right )&=3 t^{2}-3 x \left (t \right )-3 y \left (t \right )-8 t \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve([2*diff(x(t),t)+diff(y(t),t)+x(t)+y(t)=t^2+4*t,diff(x(t),t)+diff(y(t),t)+2*x(t)+2*y(t)=2*t^2-2*t],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{-2 t}}{2}+2 t^{2}+t +c_{2} \\ y \left (t \right ) &= -t^{2}+\frac {3 c_{1} {\mathrm e}^{-2 t}}{2}-3 t +1-c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 82
DSolve[{2*x'[t]+y'[t]+x[t]+y[t]==t^2+4*t,x'[t]+y'[t]+2*x[t]+2*y[t]==2*t^2-2*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-2 t} \left (e^{2 t} \left (4 t^2+2 t-1+3 c_1+c_2\right )-c_1-c_2\right ) \\ y(t)\to \frac {1}{2} \left (-2 t^2-6 t+3 (c_1+c_2) e^{-2 t}+3-3 c_1-c_2\right ) \\ \end{align*}