54.2.410 problem 989

Internal problem ID [12284]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 989
Date solved : Wednesday, October 01, 2025 at 01:27:56 AM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=-F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 29

ode:=diff(y(x),x) = -F(x)*(-a*y(x)^2-b*x^2)+y(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\left (\int F \left (x \right ) x d x +c_1 \right ) \sqrt {b a}\right ) x \sqrt {b a}}{a} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 42

ode=D[y[x],x] == y[x]/x - F[x]*(-(b*x^2) - a*y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{a K[1]^2+b}dK[1]=\int _1^xF(K[2]) K[2]dK[2]+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
F = Function("F") 
ode = Eq((-a*y(x)**2 - b*x**2)*F(x) + Derivative(y(x), x) - y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(a*y(x)**2 + b*x**2)*F(x) + y(x))/x cannot be solved by the factorable group method