23.28 problem 659

Internal problem ID [3398]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 23
Problem number: 659.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class G], _rational]

Solve \begin {gather*} \boxed {x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}=0} \end {gather*}

Solution by Maple

Time used: 0.019 (sec). Leaf size: 25

dsolve(x*(x+6*y(x)^2)*diff(y(x),x)+x*y(x)-3*y(x)^3 = 0,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {\LambertW \left (\frac {6 \,{\mathrm e}^{3 c_{1}}}{x^{3}}\right )}{2}+\frac {3 c_{1}}{2}}}{x} \]

Solution by Mathematica

Time used: 34.694 (sec). Leaf size: 69

DSolve[x(x+6 y[x]^2)y'[x]+x y[x]-3 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {\text {ProductLog}\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {\text {ProductLog}\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}