31.3.1 problem 2

Internal problem ID [5731]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 4
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:11:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 7.912 (sec). Leaf size: 70

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

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