23.4.245 problem 245

Internal problem ID [6547]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 245
Date solved : Tuesday, September 30, 2025 at 03:04:18 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^2 + y[x]^2)*D[y[x],{x,2}] == (1 + y[x]^2)*(-y[x] + x*D[y[x],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**2 + y(x)**2)*Derivative(y(x), (x, 2)) - (x*Derivative(y(x), x) - y(x))*(y(x)**2 + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2*Derivative(y(x), (x, 2)) + y(x)**3 +