Internal problem ID [7797]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 217.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {\left (-x^{2}+y\right ) y^{\prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 23
dsolve((y(x)-x^2)*diff(y(x),x)-x=0,y(x), singsol=all)
\[ y \relax (x ) = x^{2}+\frac {\LambertW \left (-4 c_{1} {\mathrm e}^{-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 29
DSolve[(y[x]-x^2)*y'[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+\operatorname {ProductLog}\left (-e^{-2 x^2-1+c_1}\right )\right ) \\ \end{align*}