Internal problem ID [2321]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page
575
Problem number: Problem 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y-8 \,{\mathrm e}^{-x}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 38
dsolve(diff(y(x),x$3)+9*diff(y(x),x$2)+24*diff(y(x),x)+16*y(x)=8*exp(-x)+1,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{16}-\frac {16 \,{\mathrm e}^{-x}}{27}+\frac {8 x \,{\mathrm e}^{-x}}{9}+{\mathrm e}^{-4 x} c_{1}+c_{2} {\mathrm e}^{-x}+c_{3} x \,{\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 39
DSolve[y'''[x]+9*y''[x]+24*y'[x]+16*y[x]==8*Exp[-x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16}+e^{-4 x} \left (c_2 x+e^{3 x} \left (\frac {8 x}{9}-\frac {16}{27}+c_3\right )+c_1\right ) \\ \end{align*}