Internal problem ID [10214]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1891.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\left (t \right )+6 x \left (t \right )+7 y \left (t \right )&=0\\ y^{\prime \prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right )&=2 t \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 64
dsolve([diff(x(t),t,t)+6*x(t)+7*y(t)=0,diff(y(t),t,t)+3*x(t)+2*y(t)=2*t],singsol=all)
\begin{align*} x \left (t \right ) &= -c_{1} {\mathrm e}^{t}+\frac {7 c_{2} \cos \left (3 t \right )}{3}-c_{3} {\mathrm e}^{-t}+\frac {7 c_{4} \sin \left (3 t \right )}{3}+\frac {14 t}{9} \\ y \left (t \right ) &= -\frac {4 t}{3}+c_{1} {\mathrm e}^{t}+c_{2} \cos \left (3 t \right )+c_{3} {\mathrm e}^{-t}+c_{4} \sin \left (3 t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.247 (sec). Leaf size: 200
DSolve[{x''[t]+6*x[t]+7*y[t]==0,y''[t]+3*x[t]+2*y[t]==2*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{180} e^{-t} \left (280 e^t t+27 c_1 e^{2 t}+27 c_2 e^{2 t}-63 c_3 e^{2 t}-63 c_4 e^{2 t}+126 (c_1+c_3) e^t \cos (3 t)+42 (c_2+c_4) e^t \sin (3 t)+27 c_1-27 c_2-63 c_3+63 c_4\right ) \\ y(t)\to \frac {1}{60} e^{-t} \left (-80 e^t t-9 c_1 e^{2 t}-9 c_2 e^{2 t}+21 c_3 e^{2 t}+21 c_4 e^{2 t}+18 (c_1+c_3) e^t \cos (3 t)+6 (c_2+c_4) e^t \sin (3 t)-9 c_1+9 c_2+21 c_3-21 c_4\right ) \\ \end{align*}