28.2.9 problem 9

Internal problem ID [4452]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 9
Date solved : Monday, January 27, 2025 at 09:17:50 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+2*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 27

DSolve[D[y[x],{x,4}]-2*D[y[x],{x,3}]+2*D[y[x],{x,2}]-2*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_4 x+c_3)+c_1 \cos (x)+c_2 \sin (x) \]