Internal problem ID [3872]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 19
dsolve((3*x/y(x)^3)+(1/y(x)^2-3*x^2/y(x)^4)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {-\frac {3}{\LambertW \left (-3 c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 60.08 (sec). Leaf size: 61
DSolve[(3*x/y[x]^3)+(1/y[x]^2-3*x^2/y[x]^4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {3} x}{\sqrt {\text {ProductLog}\left (-3 e^{-2 c_1} x^2\right )}} \\ y(x)\to \frac {i \sqrt {3} x}{\sqrt {\text {ProductLog}\left (-3 e^{-2 c_1} x^2\right )}} \\ \end{align*}