28.2.6 problem 6

Internal problem ID [4449]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 6
Date solved : Monday, January 27, 2025 at 09:17:49 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 40

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

\[ y(x)\to e^{-x} \left (\left (c_4 e^{2 x}+c_1\right ) \cos (x)+\left (c_3 e^{2 x}+c_2\right ) \sin (x)\right ) \]