Internal problem ID [10197]
Internal file name [OUTPUT/9144_Monday_June_06_2022_06_44_54_AM_80663173/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1875.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right ) f \left (t \right ) a -y \left (t \right ) f \left (t \right ) b +g \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) f \left (t \right ) c -f \left (t \right ) y \left (t \right ) d +h \left (t \right ) \end {align*}
Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✓ Solution by Maple
Time used: 3.25 (sec). Leaf size: 3922
dsolve([diff(x(t),t)+(a*x(t)+b*y(t))*f(t)=g(t),diff(y(t),t)+(c*x(t)+d*y(t))*f(t)=h(t)],singsol=all)
\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.274 (sec). Leaf size: 3095
DSolve[{x'[t]+(a*x[t]+b*y[t])*f[t]==g[t],y'[t]+(c*x[t]+d*y[t])*f[t]==h[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Too large to display