Internal problem ID [7800]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 220.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime } y-x y^{2}-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(2*y(x)*diff(y(x),x)-x*y(x)^2-x^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{\frac {x^{2}}{2}} c_{1}-x^{2}-2} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{\frac {x^{2}}{2}} c_{1}-x^{2}-2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.497 (sec). Leaf size: 57
DSolve[2*y[x]*y'[x]-x*y[x]^2-x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2+c_1 e^{\frac {x^2}{2}}-2} \\ y(x)\to \sqrt {-x^2+c_1 e^{\frac {x^2}{2}}-2} \\ \end{align*}