60.1.477 problem 480

Internal problem ID [10491]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 480
Date solved : Monday, January 27, 2025 at 08:15:01 PM
CAS classification : [_rational]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved