Internal problem ID [3122]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 374.
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 }-x^{2}-\left (1-2 y x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(x*(-x^3+1)*diff(y(x),x) = x^2+(1-2*x*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (x +c_{1}\right )}{c_{1} x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.336 (sec). Leaf size: 31
DSolve[x(1-x^3)y'[x]==x^2+(1-2 x y[x])y[x],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*}