Internal problem ID [15545]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 23.2 The method of undetermined
coefficients. Exercises page 239
Problem number: 822.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\sin \left (t \right )-{\mathrm e}^{-t}-y \left (t \right )\\ y^{\prime }\left (t \right )&=-\sin \left (t \right )+2 \,{\mathrm e}^{-t} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 39
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)=sin(t)],singsol=all)
\begin{align*} x \left (t \right ) &= -\sin \left (t \right )-{\mathrm e}^{-t}-\cos \left (t \right )+c_{1} t +c_{2} \\ y \left (t \right ) &= \cos \left (t \right )-2 \,{\mathrm e}^{-t}-c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 43
DSolve[{x'[t]+y'[t]+y[t]==Exp[-t],2*x'[t]+y'[t]+2*y[t]==Sin[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{-t}-\sin (t)-\cos (t)-c_2 t+c_1 \\ y(t)\to -2 e^{-t}+\cos (t)+c_2 \\ \end{align*}