40.3.31 problem 26 (e)

Internal problem ID [6635]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (e)
Date solved : Monday, January 27, 2025 at 02:16:26 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.266 (sec). Leaf size: 38

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

\[ y = \frac {{\mathrm e}^{\frac {3 c_1}{2}} \sqrt {6}}{6 x \sqrt {\frac {{\mathrm e}^{3 c_1}}{x^{3} \operatorname {LambertW}\left (\frac {6 \,{\mathrm e}^{3 c_1}}{x^{3}}\right )}}} \]

✓ Solution by Mathematica

Time used: 3.447 (sec). Leaf size: 73

DSolve[(3*y[x]^3-x*y[x])-(x^2+6*x*y[x]^2)*D[y[x],x]==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*}