Internal problem ID [10194]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1871.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-27-5 x \left (t \right )-y \left (t \right )+7 \,{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=12+2 x \left (t \right )-3 y \left (t \right )-3 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 71
dsolve([4*diff(x(t),t)+9*diff(y(t),t)+2*x(t)+31*y(t)=exp(t),3*diff(x(t),t)+7*diff(y(t),t)+x(t)+24*y(t)=3],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-4 t} \sin \left (t \right ) c_{2} +{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1} -\frac {93}{17}+\frac {31 \,{\mathrm e}^{t}}{26} \\ y \left (t \right ) &= -{\mathrm e}^{-4 t} \sin \left (t \right ) c_{2} -{\mathrm e}^{-4 t} \cos \left (t \right ) c_{2} -{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1} +{\mathrm e}^{-4 t} \sin \left (t \right ) c_{1} -\frac {2 \,{\mathrm e}^{t}}{13}+\frac {6}{17} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.463 (sec). Leaf size: 79
DSolve[{4*x'[t]+9*y'[t]+2*x[t]+31*y[t]==Exp[t],3*x'[t]+7*y'[t]+x[t]+24*y[t]==3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {31 e^t}{26}+c_1 e^{-4 t} \cos (t)-(c_1+c_2) e^{-4 t} \sin (t)-\frac {93}{17} \\ y(t)\to -\frac {2 e^t}{13}+c_2 e^{-4 t} \cos (t)+(2 c_1+c_2) e^{-4 t} \sin (t)+\frac {6}{17} \\ \end{align*}