Internal problem ID [10195]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1872.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-y \left (t \right )+7 \,{\mathrm e}^{t}-9 \,{\mathrm e}^{2 t}\\ y^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right )-3 \,{\mathrm e}^{t}+4 \,{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 65
dsolve([4*diff(x(t),t)+9*diff(y(t),t)+11*x(t)+31*y(t)=exp(t),3*diff(x(t),t)+7*diff(y(t),t)+8*x(t)+24*y(t)=exp(2*t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} t c_{1} +\frac {31 \,{\mathrm e}^{t}}{25}-\frac {49 \,{\mathrm e}^{2 t}}{36} \\ y \left (t \right ) &= \frac {19 \,{\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 {11 \,{\mathrm e}^{t}}{25} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.305 (sec). Leaf size: 76
DSolve[{4*x'[t]+9*y'[t]+11*x[t]+31*y[t]==Exp[t],3*x'[t]+7*y'[t]+8*x[t]+24*y[t]==Exp[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {31 e^t}{25}-\frac {49 e^{2 t}}{36}-e^{-4 t} (c_1 (t-1)+c_2 t) \\ y(t)\to -\frac {11 e^t}{25}+\frac {19 e^{2 t}}{36}+e^{-4 t} ((c_1+c_2) t+c_2) \\ \end{align*}