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]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=\frac {4}{1+{\mathrm e}^{-x}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=4/(1+exp(-x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (\left (4 \,{\mathrm e}^{x}+4\right ) \ln \left (1+{\mathrm e}^{x}\right )+\left (-4 \,{\mathrm e}^{x}-4\right ) \ln \left ({\mathrm e}^{x}\right )+{\mathrm e}^{x} c_{1} +c_{2} -4\right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 34
DSolve[y''[x]-3*y'[x]+2*y[x]==4/(1+Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (8 \left (e^x+1\right ) \text {arctanh}\left (2 e^x+1\right )+c_2 e^x-4+c_1\right ) \]