Internal problem ID [243]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 48.
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 }-8 y-3 \,{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=3*exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{4 x} c_{2}+{\mathrm e}^{-2 x} c_{1}-\frac {{\mathrm e}^{-2 x} x}{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 30
DSolve[y''[x]-2*y'[x]-8*y[x]==3*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (-\frac {x}{2}+c_2 e^{6 x}-\frac {1}{12}+c_1\right ) \\ \end{align*}