Internal problem ID [11841]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\frac {1}{{\mathrm e}^{x}+1}} \]
✓ 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)=1/(1+exp(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\ln \left ({\mathrm e}^{x}+1\right ) \left ({\mathrm e}^{x}+1\right )-\ln \left ({\mathrm e}^{x}\right ) {\mathrm e}^{x}+\left (c_{2} +x \right ) {\mathrm e}^{x}-c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 34
DSolve[y''[x]+3*y'[x]+2*y[x]==1/(1+Exp[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (\left (e^x+1\right ) \log \left (e^x+1\right )+(-1+c_2) e^x+c_1\right ) \]