15.1.16 problem 16

Internal problem ID [2856]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 16
Date solved : Monday, January 27, 2025 at 06:20:15 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

dsolve(y(x)+x*diff(y(x),x)=x*y(x)*(diff(y(x),x)-1),y(x), singsol=all)
 

\[ y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x}}{c_1 x}\right ) \]

✓ Solution by Mathematica

Time used: 2.911 (sec). Leaf size: 28

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

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