Internal problem ID [10213]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1881.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )&=f \left (t \right )\\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )&=g \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 48
dsolve([diff(x(t),t)+diff(y(t),t)+y(t)=f(t),diff(x(t),t$2)+diff(y(t),t$2)+diff(y(t),t)+x(t)+y(t)=g(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {d}{d t}f \left (t \right )-f \left (t \right )-\frac {d^{2}}{d t^{2}}f \left (t \right )+\frac {d}{d t}g \left (t \right )+g \left (t \right ) \] \[ y \left (t \right ) = f \left (t \right )+\frac {d^{2}}{d t^{2}}f \left (t \right )-\frac {d}{d t}g \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 44
DSolve[{x'[t]+y'[t]+y[t]==f[t],x''[t]+y''[t]+y'[t]+x[t]+y[t]==g[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -f''(t)-f'(t)-f(t)+g'(t)+g(t) y(t)\to f''(t)+f(t)-g'(t) \end{align*}