Internal problem ID [11934]
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: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-t +2 \,{\mathrm e}^{3 t}+6 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+t -{\mathrm e}^{3 t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 66
dsolve([diff(x(t),t)+diff(y(t),t)-x(t)-6*y(t)=exp(3*t),diff(x(t),t)+2*diff(y(t),t)-2*x(t)-6*y(t)=t],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\sqrt {6}\, t} c_{2} +{\mathrm e}^{-\sqrt {6}\, t} c_{1} -t +\frac {1}{6} \\ y \left (t \right ) &= \frac {\sqrt {6}\, {\mathrm e}^{\sqrt {6}\, t} c_{2}}{6}-\frac {\sqrt {6}\, {\mathrm e}^{-\sqrt {6}\, t} c_{1}}{6}-\frac {1}{6}+\frac {t}{6}-\frac {{\mathrm e}^{3 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 8.119 (sec). Leaf size: 142
DSolve[{x'[t]+y'[t]-x[t]-6*y[t]==Exp[3*t],x'[t]+2*y'[t]-2*x[t]-6*y[t]==t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{6} \left (-6 t+3 \left (c_1-\sqrt {6} c_2\right ) e^{-\sqrt {6} t}+3 \left (c_1+\sqrt {6} c_2\right ) e^{\sqrt {6} t}+1\right ) \\ y(t)\to \frac {1}{12} e^{-\sqrt {6} t} \left (2 e^{\sqrt {6} t} (t-1)-4 e^{\left (3+\sqrt {6}\right ) t}+\left (\sqrt {6} c_1+6 c_2\right ) e^{2 \sqrt {6} t}-\sqrt {6} c_1+6 c_2\right ) \\ \end{align*}