Internal problem ID [3885]
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]
\[ \boxed {x \left (1-y^{2}\right ) y^{\prime }-\left (x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*(1-y(x)^2)*diff(y(x),x) = (x^2+1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {-\frac {1}{\operatorname {LambertW}\left (-{\mathrm e}^{x^{2}} c_{1} x^{2}\right )}}} \]
✓ Solution by Mathematica
Time used: 5.963 (sec). Leaf size: 62
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 {W\left (x^2 \left (-e^{x^2-2 c_1}\right )\right )} y(x)\to i \sqrt {W\left (x^2 \left (-e^{x^2-2 c_1}\right )\right )} y(x)\to 0 \end{align*}