Internal problem ID [2830]
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]]
\[ \boxed {y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y=8 \,{\mathrm e}^{-x}+1} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {1}{16}-\frac {16 \,{\mathrm e}^{-x}}{27}+\frac {8 x \,{\mathrm e}^{-x}}{9}+c_{1} {\mathrm e}^{-4 x}+{\mathrm e}^{-x} c_{2} +c_{3} x \,{\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.076 (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]
\[ y(x)\to e^{-4 x} (c_2 x+c_1)+e^{-x} \left (\frac {8 x}{9}-\frac {16}{27}+c_3\right )+\frac {1}{16} \]