Internal problem ID [4249]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (1+y\right ) y^{\prime }-y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 7
dsolve([(1+y(x))*diff(y(x),x)=y(x),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \LambertW \left ({\mathrm e}^{x}\right ) \]
✓ Solution by Mathematica
Time used: 19.854 (sec). Leaf size: 9
DSolve[{(1+y[x])*y'[x]==y[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ProductLog}\left (e^x\right ) \\ \end{align*}