Internal problem ID [4248]
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]
\[ \boxed {\left (1+y\right ) y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 7
dsolve([(1+y(x))*diff(y(x),x)=y(x),y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left ({\mathrm e}^{x}\right ) \]
✓ Solution by Mathematica
Time used: 2.168 (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 W\left (e^x\right ) \\ \end{align*}