60.1.507 problem 510

Internal problem ID [10521]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 510
Date solved : Monday, January 27, 2025 at 08:45:02 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(x^2*(x^2*y(x)^4-1)*diff(y(x),x)^2+2*x^3*y(x)^3*(y(x)^2-x^2)*diff(y(x),x)-y(x)^2*(x^4*y(x)^2-1)=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^4*y[x]^2)) + 2*x^3*y[x]^3*(-x^2 + y[x]^2)*D[y[x],x] + x^2*(-1 + x^2*y[x]^4)*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved