Internal problem ID [4307]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 9.
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-2 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}+x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 20
DSolve[y''[x]+2*y'[x]+y[x]==2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x (x+c_2)+c_1) \\ \end{align*}