32.3.2 problem Exact Differential equations. Exercise 9.5, page 79

Internal problem ID [5800]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.5, page 79
Date solved : Monday, January 27, 2025 at 01:19:40 PM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 18

dsolve((2*x*y(x)+1)/y(x)+(y(x)-x)/y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.989 (sec). Leaf size: 30

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

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