Internal problem ID [2010]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-4 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=4*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+x \,{\mathrm e}^{-x} c_{1}+2 x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 22
DSolve[y''[x]+2*y'[x]+y[x]==4*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x (2 x+c_2)+c_1) \\ \end{align*}