28.2.10 problem 10

Internal problem ID [4453]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 10
Date solved : Monday, January 27, 2025 at 09:17:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-5*diff(y(x),x$3)+5*diff(y(x),x$2)+5*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[D[y[x],{x,4}]-5*D[y[x],{x,3}]+5*D[y[x],{x,2}]+5*D[y[x],x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-x}+c_2 e^x+c_3 e^{2 x}+c_4 e^{3 x} \]