54.1.229 problem 234

Internal problem ID [11543]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 234
Date solved : Tuesday, September 30, 2025 at 08:59:03 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y y^{\prime }-y^{2}+x y+x^{3}-2 x^{2}&=0 \end{align*}

✗ Maple

ode:=x*y(x)*diff(y(x),x)-y(x)^2+x*y(x)+x^3-2*x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*y[x]*D[y[x],x]-y[x]^2+x*y[x]+x^3-2*x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3 - 2*x**2 + x*y(x)*Derivative(y(x), x) + x*y(x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE x**2/y(x) - 2*x/y(x) + Derivative(y(x), x) + 1 - y(x)/x cannot be solved by the factorable group method