15.19.3 problem 3

Internal problem ID [3287]
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 : 3
Date solved : Sunday, March 30, 2025 at 01:31:28 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} 1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \end{align*}

✗ Maple

ode:=1+(2*y(x)-x^2)*diff(y(x),x)^2-2*x^2*y(x)*diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out