Internal problem ID [10212]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1889.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\left (t \right )+x \left (t \right )+y \left (t \right )&=-5\\ y^{\prime \prime }\left (t \right )-4 x \left (t \right )-3 y \left (t \right )&=-3 \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 72
dsolve([diff(x(t),t,t)+x(t)+y(t)=-5,diff(y(t),t,t)-4*x(t)-3*y(t)=-3],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{t}}{2}-\frac {c_{2} {\mathrm e}^{-t}}{2}+\frac {c_{3} {\mathrm e}^{t}}{2}-\frac {c_{3} t \,{\mathrm e}^{t}}{2}-\frac {c_{4} {\mathrm e}^{-t} t}{2}-\frac {c_{4} {\mathrm e}^{-t}}{2}+18 \\ y \left (t \right ) &= -23+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-t}+c_{3} t \,{\mathrm e}^{t}+c_{4} {\mathrm e}^{-t} t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.586 (sec). Leaf size: 151
DSolve[{x''[t]+x[t]+y[t]==-5,y''[t]-4*x[t]-3*y[t]==-3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} e^{-t} \left (72 e^t+2 c_1 (t+1)-2 c_2 t+c_3 t-c_4 t+e^{2 t} (-2 c_1 (t-1)-2 c_2 (t-2)-c_3 t-c_4 t+c_4)-4 c_2-c_4\right ) \\ y(t)\to \frac {1}{2} e^{-t} \left (-46 e^t+(-2 c_1+2 c_2-c_3+c_4) t+e^{2 t} ((2 c_1+2 c_2+c_3+c_4) t-2 c_2+c_3)+2 c_2+c_3\right ) \\ \end{align*}