Internal problem ID [15552]
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 23.3 dAlemberts method. Exercises
page 243
Problem number: 829.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+\sin \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve([diff(x(t),t)=2*x(t)+4*y(t)+cos(t),diff(y(t),t)=-x(t)-2*y(t)+sin(t)],singsol=all)
\begin{align*} x \left (t \right ) &= -2 \cos \left (t \right )-3 \sin \left (t \right )+c_{1} t +c_{2} \\ y \left (t \right ) &= 2 \sin \left (t \right )+\frac {c_{1}}{4}-\frac {c_{1} t}{2}-\frac {c_{2}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 46
DSolve[{x'[t]==2*x[t]+4*y[t]+Cos[t],y'[t]==-x[t]-2*y[t]+Sin[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -3 \sin (t)-2 \cos (t)+2 c_1 t+4 c_2 t+c_1 \\ y(t)\to 2 \sin (t)-(c_1+2 c_2) t+c_2 \\ \end{align*}