10.6.15 problem 15

Internal problem ID [1232]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 15
Date solved : Monday, January 27, 2025 at 04:46:16 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \frac {c_1 \,{\mathrm e}^{x}}{\left (1+{\mathrm e}^{x}\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 23

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

\begin{align*} y(x)\to \frac {c_1 e^x}{\left (e^x+1\right )^2} \\ y(x)\to 0 \\ \end{align*}