9.19.6 problem 6

Internal problem ID [3290]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 06:32:35 AM
CAS classification : [_rational]

\begin{align*} x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime }&=y \end{align*}

✗ Maple

ode:=x*y(x)*diff(y(x),x)^2+(x*y(x)-1)*diff(y(x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*y[x]*D[y[x],x]^2+(x*y[x]-1)*D[y[x],x]==y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)*Derivative(y(x), x)**2 + (x*y(x) - 1)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out