Internal problem ID [9450]
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 }\relax (t )&=-5 x \relax (t )-y \relax (t )-27+7 \,{\mathrm e}^{t}\\ y^{\prime }\relax (t )&=2 x \relax (t )-3 y \relax (t )+12-3 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.097 (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},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = {\mathrm e}^{-4 t} \sin \relax (t ) c_{2}+{\mathrm e}^{-4 t} \cos \relax (t ) c_{1}-\frac {93}{17}+\frac {31 \,{\mathrm e}^{t}}{26} \] \[ y \relax (t ) = -{\mathrm e}^{-4 t} \sin \relax (t ) c_{2}-{\mathrm e}^{-4 t} \cos \relax (t ) c_{2}-{\mathrm e}^{-4 t} \cos \relax (t ) c_{1}+{\mathrm e}^{-4 t} \sin \relax (t ) c_{1}-\frac {2 \,{\mathrm e}^{t}}{13}+\frac {6}{17} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 72
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}+e^{-4 t} (c_1 \cos (t)-(c_1+c_2) \sin (t))-\frac {93}{17} \\ y(t)\to -\frac {2 e^t}{13}+e^{-4 t} (2 c_1 \sin (t)+c_2 (\sin (t)+\cos (t)))+\frac {6}{17} \\ \end{align*}