71.10.3 problem 3

Internal problem ID [14498]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 06:42:40 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

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

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