Internal problem ID [9472]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1897.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} 2 x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )&=2 t\\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )&=\sinh \left (2 t \right ) \end {align*}
✓ Solution by Maple
Time used: 1.0 (sec). Leaf size: 104
dsolve([diff(x(t),t,t)+diff(y(t),t,t)+diff(y(t),t)=sinh(2*t),2*diff(x(t),t,t)+diff(y(t),t,t)=2*t],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {t^{2}}{4}+c_{4} t +\frac {t^{3}}{6}+\frac {t \sinh \left (2 t \right )}{4}-\frac {\cosh \left (2 t \right )}{8}-\frac {t \cosh \left (2 t \right )}{4}+\frac {\cosh \left (2 t \right ) c_{3}}{4}-\frac {c_{3} \sinh \left (2 t \right )}{4}+c_{1} t +c_{2} \] \[ y \left (t \right ) = \frac {t}{2}-\frac {t \sinh \left (2 t \right )}{2}+\frac {\cosh \left (2 t \right )}{4}+\frac {c_{3} \sinh \left (2 t \right )}{2}+\frac {t \cosh \left (2 t \right )}{2}-\frac {\cosh \left (2 t \right ) c_{3}}{2}-\frac {t^{2}}{2}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 110
DSolve[{x''[t]+y''[t]+y'[t]==Sinh[2*t],2*x''[t]+y''[t]==2*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{48} \left (-3 e^{2 t}-6 e^{-2 t} (2 t+1-2 c_4)+4 t (t (2 t+3)-3+12 c_2+6 c_4)+6+48 c_1-12 c_4\right ) \\ y(t)\to \frac {1}{8} e^{-2 t} \left (4 t+e^{4 t}+e^{2 t} (-4 (t-1) t-2+8 c_3+4 c_4)+2-4 c_4\right ) \\ \end{align*}