Internal problem ID [3429]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 691.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{3} y^{\prime } x -\left (1-x^{2}\right ) \left (1+y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.163 (sec). Leaf size: 29
dsolve(x*y(x)^3*diff(y(x),x) = (-x^2+1)*(1+y(x)^2),y(x), singsol=all)
\[ \frac {x^{2}}{2}-\ln \relax (x )+\frac {y \relax (x )^{2}}{2}-\frac {\ln \left (1+y \relax (x )^{2}\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 61
DSolve[x y[x]^3 y'[x]==(1-x^2)(1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1-\text {ProductLog}\left (-\frac {e^{x^2-1-2 c_1}}{x^2}\right )} \\ y(x)\to \sqrt {-1-\text {ProductLog}\left (-\frac {e^{x^2-1-2 c_1}}{x^2}\right )} \\ \end{align*}