31.2.3 problem 3

Internal problem ID [5724]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:11:37 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 22

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)
 

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

✓ Solution by Mathematica

Time used: 6.744 (sec). Leaf size: 70

DSolve[(3*x/y[x]^3)+(1/y[x]^2-3*x^2/y[x]^4)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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