12.18.32 problem section 9.2, problem 43(e)

Internal problem ID [2146]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 43(e)
Date solved : Monday, January 27, 2025 at 05:42:49 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+64 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 41

dsolve(diff(y(x),x$4)+64*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 44

DSolve[D[y[x],{x,4}]+64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (\left (c_4 e^{4 x}+c_1\right ) \cos (2 x)+\left (c_3 e^{4 x}+c_2\right ) \sin (2 x)\right ) \]