Internal problem ID [5292]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {3 y^{3}-x y-\left (x^{2}+6 x y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {3 c_{1}}{2}} \sqrt {6}}{6 x \sqrt {\frac {{\mathrm e}^{3 c_{1}}}{x^{3} \operatorname {LambertW}\left (\frac {6 \,{\mathrm e}^{3 c_{1}}}{x^{3}}\right )}}} \]
✓ Solution by Mathematica
Time used: 3.943 (sec). Leaf size: 69
DSolve[(3*y[x]^3-x*y[x])-(x^2+6*x*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}