64.10.18 problem 18

Internal problem ID [13424]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 05:42:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 25

dsolve(diff(y(x),x$4)+8*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_{2} \right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (c_{3} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,4}]+8*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos (2 x)+(c_4 x+c_3) \sin (2 x) \]