Internal problem ID [3382]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 643.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (2 x^{2}+y^{2}\right ) y^{\prime }-\left (2 x^{2}+3 y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(x*(2*x^2+y(x)^2)*diff(y(x),x) = (2*x^2+3*y(x)^2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left (\frac {2 \,{\mathrm e}^{-4 c_{1}}}{x^{4}}\right )}{2}+2 c_{1}} x^{3} \]
✓ Solution by Mathematica
Time used: 51.011 (sec). Leaf size: 56
DSolve[x(2 x^2+y[x]^2)y'[x]==(2 x^2+3 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2} x}{\sqrt {\text {ProductLog}\left (\frac {2 e^{-2 c_1}}{x^4}\right )}} \\ y(x)\to \frac {\sqrt {2} x}{\sqrt {\text {ProductLog}\left (\frac {2 e^{-2 c_1}}{x^4}\right )}} \\ \end{align*}