Internal problem ID [7762]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 182.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*(x^3-1)*diff(y(x),x) - 2*x*y(x)^2 + y(x) + x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x +c_{1}\right ) x}{c_{1} x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.368 (sec). Leaf size: 31
DSolve[x*(x^3-1)*y'[x] - 2*x*y[x]^2 + y[x] + x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (1+2 c_1 x)}{x^2+2 c_1} \\ y(x)\to x^2 \\ \end{align*}