Internal problem ID [3411]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 672.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{3} \left (1+y^{2}\right ) y^{\prime }+3 y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 14
dsolve(x^3*(1+y(x)^2)*diff(y(x),x)+3*x^2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {\frac {1}{\LambertW \left (\frac {c_{1}}{x^{6}}\right )}}} \]
✓ Solution by Mathematica
Time used: 33.855 (sec). Leaf size: 46
DSolve[x^3(1+y[x]^2)y'[x]+3 x^2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\text {ProductLog}\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to \sqrt {\text {ProductLog}\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to 0 \\ \end{align*}