20.6.19 problem Problem 41

Internal problem ID [3714]
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 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 41
Date solved : Monday, January 27, 2025 at 07:55:48 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=24 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

dsolve(diff(y(x),x$3)+diff(y(x),x$2)-10*diff(y(x),x)+8*y(x)=24*exp(-3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (5 c_3 \,{\mathrm e}^{6 x}+5 \,{\mathrm e}^{5 x} c_{1} +6 \,{\mathrm e}^{x}+5 c_{2} \right ) {\mathrm e}^{-4 x}}{5} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]-10*D[y[x],x]+8*y[x]==24*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 e^{-3 x}}{5}+c_1 e^{-4 x}+c_2 e^x+c_3 e^{2 x} \]