35.2.9 problem 9

Internal problem ID [6101]
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
Date solved : Monday, January 27, 2025 at 01:36:11 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 7

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

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

✓ Solution by Mathematica

Time used: 1.967 (sec). Leaf size: 9

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

\[ y(x)\to W\left (e^x\right ) \]