77.23.27 problem 27

Internal problem ID [20593]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 27
Date solved : Thursday, October 02, 2025 at 06:14:47 PM
CAS classification : [_rational]

\begin{align*} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-y x&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out