28.2.11 problem 11

Internal problem ID [4454]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 11
Date solved : Monday, January 27, 2025 at 09:17:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$5)-6*diff(y(x),x$4)+9*diff(y(x),x$3)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (x c_5 +c_4 \right ) {\mathrm e}^{3 x}+c_3 \,x^{2}+c_{2} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 35

DSolve[D[y[x],{x,5}]-6*D[y[x],{x,4}]+9*D[y[x],{x,3}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{27} e^{3 x} (c_2 (x-1)+c_1)+x (c_5 x+c_4)+c_3 \]