Internal problem ID [3379]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 640.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational]
Solve \begin {gather*} \boxed {x \left (x^{2}+y^{2}\right ) y^{\prime }-\left (x^{2}+x^{4}+y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(x*(x^2+y(x)^2)*diff(y(x),x) = (x^2+x^4+y(x)^2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {\LambertW \left ({\mathrm e}^{x^{2}} {\mathrm e}^{2 c_{1}}\right )}{2}+\frac {x^{2}}{2}+c_{1}} x \]
✓ Solution by Mathematica
Time used: 60.104 (sec). Leaf size: 44
DSolve[x(x^2+y[x]^2)y'[x]==(x^2+x^4+y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {\text {ProductLog}\left (e^{x^2+2 c_1}\right )} \\ y(x)\to x \sqrt {\text {ProductLog}\left (e^{x^2+2 c_1}\right )} \\ \end{align*}