3.2 problem Exact Differential equations. Exercise 9.5, page 79

Internal problem ID [3948]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _exact, _rational, [_Abel, 2nd type, class A]]

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

Solution by Maple

Time used: 0.094 (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)
 

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

Solution by Mathematica

Time used: 60.112 (sec). Leaf size: 24

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

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