Internal problem ID [1875]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve((x*y(x)^2+x)+(x^2*y(x)-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (x^{2}-1\right ) \left (-x^{2}+c_{1}\right )}}{x^{2}-1} \\ y \relax (x ) = -\frac {\sqrt {\left (x^{2}-1\right ) \left (-x^{2}+c_{1}\right )}}{x^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.403 (sec). Leaf size: 133
DSolve[(x*y[x]^2+x)+(x^2*y[x]-y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2+1-e^{2 c_1}}}{\sqrt {x^2-1}} \\ y(x)\to \frac {\sqrt {-x^2+1-e^{2 c_1}}}{\sqrt {x^2-1}} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to -\frac {\sqrt {1-x^2}}{\sqrt {x^2-1}} \\ y(x)\to \frac {\sqrt {1-x^2}}{\sqrt {x^2-1}} \\ \end{align*}