54.10.3 problem 1915

Internal problem ID [13137]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1915
Date solved : Wednesday, October 01, 2025 at 03:36:39 AM
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*}

✗ Maple

ode:=[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)))]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={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]))}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
Alpha = symbols("Alpha") 
BETA = symbols("BETA") 
a = symbols("a") 
b = symbols("b") 
p = symbols("p") 
q = symbols("q") 
x = Function("x") 
y = Function("y") 
ode=[Eq((-Alpha - a*(p*x(t) + q*y(t)))*x(t) + Derivative(x(t), t),0),Eq((-BETA - b*(p*x(t) + q*y(t)))*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out