Internal problem ID [11938]
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: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2+x \left (t \right )-3 y \left (t \right )+4 t\\ y^{\prime }\left (t \right )&=4-3 x \left (t \right )+y \left (t \right )-4 t \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 40
dsolve([2*diff(x(t),t)+diff(y(t),t)+x(t)+5*y(t)=4*t,diff(x(t),t)+diff(y(t),t)+2*x(t)+2*y(t)=2],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{4 t}+c_{1} {\mathrm e}^{-2 t}-t +1 \\ y \left (t \right ) &= -c_{2} {\mathrm e}^{4 t}+c_{1} {\mathrm e}^{-2 t}+t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 80
DSolve[{2*x'[t]+y'[t]+x[t]+5*y[t]==4*t,x'[t]+y'[t]+2*x[t]+2*y[t]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-2 t} \left (-2 e^{2 t} (t-1)+(c_1-c_2) e^{6 t}+c_1+c_2\right ) \\ y(t)\to \frac {1}{2} e^{-2 t} \left (2 e^{2 t} t+(c_2-c_1) e^{6 t}+c_1+c_2\right ) \\ \end{align*}