Internal problem ID [9460]
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 }\relax (t )+y^{\prime }\relax (t )+y \relax (t )&=f \relax (t )\\ x^{\prime \prime }\relax (t )+y^{\prime \prime }\relax (t )+y^{\prime }\relax (t )+x \relax (t )+y \relax (t )&=g \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.082 (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)
\[ x \relax (t ) = -\frac {d}{d t}f \relax (t )+g \relax (t )-f \relax (t )-\frac {d^{2}}{d t^{2}}f \relax (t )+\frac {d}{d t}g \relax (t ) \] \[ y \relax (t ) = f \relax (t )+\frac {d^{2}}{d t^{2}}f \relax (t )-\frac {d}{d t}g \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.011 (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*}