Internal problem ID [8085]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 505.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{2} \left (y^{\prime }\right )^{2}-2 y^{\prime } y^{3}+2 y^{2} x -x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 52
dsolve(x*y(x)^2*diff(y(x),x)^2-2*y(x)^3*diff(y(x),x)+2*x*y(x)^2-x^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {x^{2}+c_{1}} \\ y \relax (x ) = \sqrt {c_{1} x^{2}+1}\, x \\ y \relax (x ) = -\sqrt {c_{1} x^{2}+1}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.512 (sec). Leaf size: 85
DSolve[-x^3 + 2*x*y[x]^2 - 2*y[x]^3*y'[x] + x*y[x]^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ y(x)\to -\sqrt {x^2+c_1 x^4} \\ y(x)\to \sqrt {x^2+c_1 x^4} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}