Internal problem ID [1157]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-\frac {4}{{\mathrm e}^{-x}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=4/(1+exp(-x)),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1} {\mathrm e}^{x}-4 \ln \left ({\mathrm e}^{x}\right )-4 \ln \left ({\mathrm e}^{x}\right ) {\mathrm e}^{x}+4 \ln \left (1+{\mathrm e}^{x}\right ) \left (1+{\mathrm e}^{x}\right )-4+c_{2}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 34
DSolve[y''[x]-3*y'[x]+2*y[x]==4/(1+Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (8 \left (e^x+1\right ) \tanh ^{-1}\left (2 e^x+1\right )+c_2 e^x-4+c_1\right ) \\ \end{align*}