Internal problem ID [11942]
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: 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {7 x \left (t \right )}{2}-\frac {9 y \left (t \right )}{2}+\frac {{\mathrm e}^{t}}{2}\\ y^{\prime }\left (t \right )&=\frac {3 x \left (t \right )}{2}+\frac {5 y \left (t \right )}{2}+\frac {{\mathrm e}^{t}}{2} \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 45
dsolve([2*diff(x(t),t)+4*diff(y(t),t)+x(t)-y(t)=3*exp(t),diff(x(t),t)+diff(y(t),t)+2*x(t)+2*y(t)=exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t}+c_{1} {\mathrm e}^{-2 t}-{\mathrm e}^{t} t \\ y \left (t \right ) &= -c_{2} {\mathrm e}^{t}-\frac {c_{1} {\mathrm e}^{-2 t}}{3}+{\mathrm e}^{t} t +\frac {{\mathrm e}^{t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 76
DSolve[{2*x'[t]+4*y'[t]+x[t]-y[t]==3*Exp[t],x'[t]+y'[t]+2*x[t]+2*y[t]==Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {3}{2} (c_1+c_2) e^{-2 t}-\frac {1}{2} e^t (2 t-1+c_1+3 c_2) \\ y(t)\to \frac {1}{6} e^t (6 t-1+3 c_1+9 c_2)-\frac {1}{2} (c_1+c_2) e^{-2 t} \\ \end{align*}