Internal problem ID [3377]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 638.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (1-y^{2}\right ) y^{\prime }-y \left (x^{2}+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 21
dsolve(x*(1-y(x)^2)*diff(y(x),x) = (x^2+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {-\frac {1}{\LambertW \left (-{\mathrm e}^{x^{2}} c_{1} x^{2}\right )}}} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 57
DSolve[x(1-y[x]^2)y'[x]==(1+x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {\text {ProductLog}\left (x^2 \left (-e^{x^2-2 c_1}\right )\right )} \\ y(x)\to i \sqrt {\text {ProductLog}\left (x^2 \left (-e^{x^2-2 c_1}\right )\right )} \\ \end{align*}