82.7.2 problem Ex. 3

Internal problem ID [18748]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 24
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:14:19 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 22

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {1}{\operatorname {LambertW}\left (-\frac {c_{1}}{x^{3}}\right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.037 (sec). Leaf size: 40

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

\begin{align*} y(x)\to 0 \\ y(x)\to -\frac {1}{x W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^3}\right )} \\ y(x)\to 0 \\ \end{align*}