Internal problem ID [7976]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 396.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+y \left (y-x \right ) y^{\prime }-x y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(diff(y(x),x)^2+y(x)*(y(x)-x)*diff(y(x),x)-x*y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ y \relax (x ) = \frac {1}{c_{1}+x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 34
DSolve[-(x*y[x]^3) + y[x]*(-x + y[x])*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x-c_1} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}