62.1.1 problem Ex 1

Internal problem ID [12798]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 8. Exact differential equations. Page 11
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:20:17 AM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.142 (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)
 

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

✓ Solution by Mathematica

Time used: 4.153 (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*}