29.23.28 problem 659

Internal problem ID [5250]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 659
Date solved : Monday, January 27, 2025 at 10:49:20 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 38

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

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

✓ Solution by Mathematica

Time used: 3.445 (sec). Leaf size: 73

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

\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2+3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2+3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}