Internal problem ID [10237]
Internal file name [OUTPUT/9184_Monday_June_06_2022_01_36_38_PM_44970814/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1915.
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 )^{2} a p +x \left (t \right ) y \left (t \right ) a q +x \left (t \right ) \alpha \\ y^{\prime }\left (t \right )&=x \left (t \right ) y \left (t \right ) b p +y \left (t \right )^{2} b q +y \left (t \right ) \beta \end {align*}
Does not currently support non linear system of equations. This is the phase plot of the system.
✗ Solution by Maple
dsolve([diff(x(t),t)=x(t)*(a*(p*x(t)+q*y(t))+alpha),diff(y(t),t)=y(t)*(beta+b*(p*x(t)+q*y(t)))],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==x[t]*(a*(p*x[t]+q*y[t])+\[Alpha]),y'[t]==y[t]*(\[Beta]+b*(p*x[t]+q*y[t]))},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Timed out