Internal problem ID [4767]
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]
\[ \boxed {\left (1+{\mathrm e}^{x}\right ) y^{\prime }+2 \,{\mathrm e}^{x} y=\left (1+{\mathrm e}^{x}\right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{3 x}+3 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{x}+3 c_{1}}{3 \left (1+{\mathrm e}^{x}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 25
DSolve[(1+Exp[x])*y'[x]+2*Exp[x]*y[x]==(1+Exp[x])*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (e^x+1\right )+\frac {c_1}{\left (e^x+1\right )^2} \]