Internal problem ID [10220]
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: 0.532 (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],singsol=all)
\begin{align*} 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 {c_{3} \sinh \left (2 t \right )}{2}-\frac {t \sinh \left (2 t \right )}{2}+\frac {\cosh \left (2 t \right )}{4}-\frac {\cosh \left (2 t \right ) c_{3}}{2}+\frac {t \cosh \left (2 t \right )}{2}-\frac {t^{2}}{2}+c_{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.393 (sec). Leaf size: 118
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 (2 \left (4 t^3+6 t^2+6 (-1+4 c_2+2 c_4) t+3+24 c_1-6 c_4\right )-3 e^{2 t}-6 e^{-2 t} (2 t+1-2 c_4)\right ) \\ y(t)\to \frac {1}{8} e^{-2 t} \left (e^{2 t} \left (-4 t^2+4 t-2+8 c_3+4 c_4\right )+4 t+e^{4 t}+2-4 c_4\right ) \\ \end{align*}