Internal problem ID [9449]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1870.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-3 y \relax (t )-{\mathrm e}^{t}+\cos \relax (t )\\ y^{\prime }\relax (t )&=4 y \relax (t )+2 \,{\mathrm e}^{t}-\cos \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 47
dsolve({diff(x(t),t)+diff(y(t),t)-y(t)=exp(t),2*diff(x(t),t)+diff(y(t),t)+2*y(t)=cos(t)},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \frac {{\mathrm e}^{4 t} c_{1}}{4}+\frac {5 \sin \relax (t )}{17}-\frac {3 \cos \relax (t )}{17}+{\mathrm e}^{t}+c_{2} \] \[ y \relax (t ) = -\frac {{\mathrm e}^{4 t} c_{1}}{3}+\frac {4 \cos \relax (t )}{17}-\frac {\sin \relax (t )}{17}-\frac {2 \,{\mathrm e}^{t}}{3} \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 71
DSolve[{x'[t]+y'[t]-y[t]==Exp[t],2*x'[t]+y'[t]+2*y[t]==Cos[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t+\frac {5 \sin (t)}{17}-\frac {3 \cos (t)}{17}-\frac {3}{4} c_2 e^{4 t}+c_1+\frac {3 c_2}{4} \\ y(t)\to -\frac {2 e^t}{3}-\frac {\sin (t)}{17}+\frac {4 \cos (t)}{17}+c_2 e^{4 t} \\ \end{align*}