15.5.3 problem 3

Internal problem ID [2939]
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
Date solved : Monday, January 27, 2025 at 06:59:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (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: 2.784 (sec). Leaf size: 26

DSolve[(x-2*x*y[x])*D[y[x],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*}