Internal problem ID [4252]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 2. Separable equations. page
398
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x y+x \right ) y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 11
dsolve([(x+x*y(x))*diff(y(x),x)+y(x)=0,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \LambertW \left (\frac {{\mathrm e}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 9.528 (sec). Leaf size: 11
DSolve[{(x+x*y[x])*y'[x]+y[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ProductLog}\left (\frac {e}{x}\right ) \\ \end{align*}