Internal problem ID [11928]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{t}\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=y \left (t \right )+{\mathrm e}^{4 t} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve([diff(x(t),t)+diff(y(t),t)-2*x(t)-4*y(t)=exp(t),diff(x(t),t)+diff(y(t),t)-y(t)=exp(4*t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-2 t} \\ y \left (t \right ) &= \frac {{\mathrm e}^{4 t}}{3}-\frac {{\mathrm e}^{t}}{3}-\frac {2 c_{1} {\mathrm e}^{-2 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 52
DSolve[{x'[t]+y'[t]-2*x[t]-4*y[t]==Exp[t],x'[t]+y'[t]-y[t]==Exp[4*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{12} (3+4 c_1) e^{-2 t} \\ y(t)\to \frac {1}{18} e^{-2 t} \left (-6 e^{3 t}+6 e^{6 t}-3-4 c_1\right ) \\ \end{align*}