Internal problem ID [1968]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x -2 y x \right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve((x-2*x*y(x))*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y = -\frac {\operatorname {LambertW}\left (-\frac {2 c_{1}}{x^{2}}\right )}{2} \]
✓ Solution by Mathematica
Time used: 2.94 (sec). Leaf size: 26
DSolve[(x-2*x*y[x])*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} W\left (-\frac {2 e^{-c_1}}{x^2}\right ) y(x)\to 0 \end{align*}