Internal problem ID [4259]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 \,{\mathrm e}^{x} y-\left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve((1+exp(x))*diff(y(x),x)+2*exp(x)*y(x)=(1+exp(x))*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{2 x}+{\mathrm e}^{x}+\frac {{\mathrm e}^{3 x}}{3}+c_{1}}{\left ({\mathrm e}^{x}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 28
DSolve[(1+Exp[x])*y'[x]+2*Exp[x]*y[x]==(1+Exp[x])*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (e^x+\frac {-1+3 c_1}{\left (e^x+1\right )^2}+1\right ) \\ \end{align*}