82.6.2 problem Ex. 2

Internal problem ID [18743]
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 22
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:14:07 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 19

dsolve((1+x*y(x))*y(x)-(1-x*y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 7.899 (sec). Leaf size: 33

DSolve[(1+x*y[x])*y[x]-(1-x*y[x])*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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