Internal problem ID [9466]
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: 0.141 (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],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{1} {\mathrm e}^{t}+\frac {7 c_{2} \cos \left (3 t \right )}{3}-c_{3} {\mathrm e}^{-t}+\frac {7 c_{4} \sin \left (3 t \right )}{3}+\frac {14 t}{9} \] \[ y \left (t \right ) = -\frac {4 t}{3}+c_{1} {\mathrm e}^{t}+c_{2} \cos \left (3 t \right )+c_{3} {\mathrm e}^{-t}+c_{4} \sin \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.793 (sec). Leaf size: 121
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}{90} (9 (3 c_1-7 c_3) \cosh (t)+9 (3 c_2-7 c_4) \sinh (t)+7 (20 t+9 (c_1+c_3) \cos (3 t)+3 (c_2+c_4) \sin (3 t))) \\ y(t)\to \frac {1}{30} (-40 t+9 (c_1+c_3) \cos (3 t)+(21 c_3-9 c_1) \cosh (t)+3 (c_2+c_4) \sin (3 t)+(21 c_4-9 c_2) \sinh (t)) \\ \end{align*}