Internal problem ID [15533]
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. Methods of integrating
nonhomogeneous linear systems with constant coefficients. Exercises page 234
Problem number: 810.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right )-{\mathrm e}^{2 t}\\ y^{\prime }\left (t \right )&=-3 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 43
dsolve([diff(x(t),t)+2*x(t)-y(t)=-exp(2*t),diff(y(t),t)+3*x(t)-2*y(t)=6*exp(2*t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t}+{\mathrm e}^{-t} c_{1} +2 \,{\mathrm e}^{2 t} \\ y \left (t \right ) &= 3 c_{2} {\mathrm e}^{t}+{\mathrm e}^{-t} c_{1} +9 \,{\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 85
DSolve[{x'[t]+2*x[t]-y[t]==-Exp[2*t],y'[t]+3*x[t]-2*y[t]==6*Exp[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-t} \left (4 e^{3 t}+(c_2-c_1) e^{2 t}+3 c_1-c_2\right ) \\ y(t)\to \frac {1}{2} e^{-t} \left (18 e^{3 t}-3 (c_1-c_2) e^{2 t}+3 c_1-c_2\right ) \\ \end{align*}