60.10.3 problem 1915

Internal problem ID [11914]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1915
Date solved : Monday, January 27, 2025 at 11:47:18 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right ) \left (a \left (p x \left (t \right )+q y \left (t \right )\right )+\alpha \right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right ) \left (\beta +b \left (p x \left (t \right )+q y \left (t \right )\right )\right ) \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]==x[t]*(a*(p*x[t]+q*y[t])+\[Alpha]),D[y[t],t]==y[t]*(\[Beta]+b*(p*x[t]+q*y[t]))},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Timed out