Internal problem ID [10191]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1868.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{2 t}\\ y^{\prime }\left (t \right )&=-x \left (t \right )-5 y \left (t \right )+{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 64
dsolve([diff(x(t),t)+3*x(t)-y(t)=exp(2*t),diff(y(t),t)+x(t)+5*y(t)=exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} t c_{1} +\frac {{\mathrm e}^{t}}{25}+\frac {7 \,{\mathrm e}^{2 t}}{36} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{2 t}}{36}-c_{2} {\mathrm e}^{-4 t}-{\mathrm e}^{-4 t} t c_{1} +{\mathrm e}^{-4 t} c_{1} +\frac {4 \,{\mathrm e}^{t}}{25} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 76
DSolve[{x'[t]+3*x[t]-y[t]==Exp[2*t],y'[t]+x[t]+5*y[t]==Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {e^t}{25}+\frac {7 e^{2 t}}{36}+e^{-4 t} (c_1 (t+1)+c_2 t) \\ y(t)\to \frac {4 e^t}{25}-\frac {e^{2 t}}{36}+e^{-4 t} (c_2-(c_1+c_2) t) \\ \end{align*}