Internal problem ID [15551]
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: 828.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 43
dsolve([diff(x(t),t)=3*x(t)+y(t)+exp(t),diff(y(t),t)=x(t)+3*y(t)-exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {c_{1} {\mathrm e}^{4 t}}{2}-{\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= \frac {c_{1} {\mathrm e}^{4 t}}{2}+{\mathrm e}^{t}-c_{2} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 70
DSolve[{x'[t]==3*x[t]+y[t]+Exp[t],y'[t]==x[t]+3*y[t]-Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^t \left ((c_1-c_2) e^t+(c_1+c_2) e^{3 t}-2\right ) \\ y(t)\to \frac {1}{2} e^t \left ((c_2-c_1) e^t+(c_1+c_2) e^{3 t}+2\right ) \\ \end{align*}