35.3.7 problem 7

Internal problem ID [6111]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:36:24 PM
CAS classification : [_linear]

\begin{align*} \left (1+{\mathrm e}^{x}\right ) y^{\prime }+2 \,{\mathrm e}^{x} y&=\left (1+{\mathrm e}^{x}\right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve((1+exp(x))*diff(y(x),x)+2*exp(x)*y(x)=(1+exp(x))*exp(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{3 x}+3 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{x}+3 c_1}{3 \left (1+{\mathrm e}^{x}\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 25

DSolve[(1+Exp[x])*D[y[x],x]+2*Exp[x]*y[x]==(1+Exp[x])*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (e^x+1\right )+\frac {c_1}{\left (e^x+1\right )^2} \]