Internal problem ID [7796]
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`]]
\[ \boxed {\left (-x^{2}+y\right ) y^{\prime }-x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((y(x)-x^2)*diff(y(x),x)-x=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{2}+\frac {\operatorname {LambertW}\left (-4 c_{1} {\mathrm e}^{-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 5.192 (sec). Leaf size: 40
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+W\left (-e^{-2 x^2-1+c_1}\right )\right ) \\ y(x)\to x^2+\frac {1}{2} \\ \end{align*}