20.12.7 problem Problem 22

Internal problem ID [3801]
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
Date solved : Monday, January 27, 2025 at 08:02:30 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y&=8 \,{\mathrm e}^{-x}+1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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)
 

\[ y \left (x \right ) = \frac {1}{16}+\frac {\left (-16+24 x +27 c_{2} \right ) {\mathrm e}^{-x}}{27}+\left (x c_3 +c_{1} \right ) {\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 39

DSolve[D[y[x],{x,3}]+9*D[y[x],{x,2}]+24*D[y[x],x]+16*y[x]==8*Exp[-x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} (c_2 x+c_1)+e^{-x} \left (\frac {8 x}{9}-\frac {16}{27}+c_3\right )+\frac {1}{16} \]