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 : Monday, January 27, 2025 at 07:31:05 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*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[1+(2*y[x]-x^2)*D[y[x],x]^2-2*x^2*y[x]*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved