60.1.528 problem 531

Internal problem ID [10542]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 531
Date solved : Monday, January 27, 2025 at 08:52:38 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)^2-(y(x)^4+x*y(x)^2+x^2)*diff(y(x),x)^2+(x*y(x)^6+x^2*y(x)^4+x^3*y(x)^2)*diff(y(x),x)-x^3*y(x)^6=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[-(x^3*y[x]^6) + (x^3*y[x]^2 + x^2*y[x]^4 + x*y[x]^6)*D[y[x],x] + D[y[x],x]^2 - (x^2 + x*y[x]^2 + y[x]^4)*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved