20.6.7 problem Problem 29

Internal problem ID [3702]
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 29
Date solved : Monday, January 27, 2025 at 07:55:38 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-18*diff(y(x),x)-40*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left ({\mathrm e}^{9 x} c_{1} +c_3 \,{\mathrm e}^{3 x}+c_{2} \right ) {\mathrm e}^{-5 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]-18*D[y[x],x]-40*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (c_2 e^{3 x}+c_3 e^{9 x}+c_1\right ) \]