Internal problem ID [4304]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+9 y-12 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=12*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-3 x} c_{2}+{\mathrm e}^{-3 x} x c_{1}+3 \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 25
DSolve[y''[x]+6*y'[x]+9*y[x]==12*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (3 e^{2 x}+c_2 x+c_1\right ) \\ \end{align*}