Internal problem ID [9468]
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 }\relax (t )+x \relax (t )+y \relax (t )&=-5\\ y^{\prime \prime }\relax (t )-4 x \relax (t )-3 y \relax (t )&=-3 \end {align*}
✓ Solution by Maple
Time used: 0.076 (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},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = 18+c_{1} {\mathrm e}^{t}+{\mathrm e}^{-t} c_{2}+c_{3} t \,{\mathrm e}^{t}+c_{4} {\mathrm e}^{-t} t \] \[ y \relax (t ) = -2 c_{1} {\mathrm e}^{t}-2 \,{\mathrm e}^{-t} c_{2}-2 c_{3} {\mathrm e}^{t}-2 c_{3} t \,{\mathrm e}^{t}-2 c_{4} {\mathrm e}^{-t} t +2 c_{4} {\mathrm e}^{-t}-23 \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 86
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}{2} ((2 c_1-(2 c_2+c_4) t) \cosh (t)+(-(2 c_1+c_3) t+4 c_2+c_4) \sinh (t)+36) \\ y(t)\to ((2 c_2+c_4) t+c_3) \cosh (t)+(2 c_1 t+c_3 t-2 c_2) \sinh (t)-23 \\ \end{align*}