60.1.503 problem 506

Internal problem ID [10517]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 506
Date solved : Monday, January 27, 2025 at 08:43:32 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved