28.2.8 problem 8

Internal problem ID [4451]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 8
Date solved : Monday, January 27, 2025 at 09:17:50 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 48

dsolve(diff(y(x),x$4)-4*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 55

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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