Internal problem ID [1871]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{2}+x +\left (y-y x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 33
dsolve((x*y(x)^2+x)+(y(x)-x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {c_{1} x^{2}-c_{1}-1} \\ y \relax (x ) = -\sqrt {c_{1} x^{2}-c_{1}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.21 (sec). Leaf size: 61
DSolve[(x*y[x]^2+x)+(y[x]-x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1+e^{2 c_1} \left (x^2-1\right )} \\ y(x)\to \sqrt {-1+e^{2 c_1} \left (x^2-1\right )} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}