7.10.18 problem 18

Internal problem ID [288]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 18
Date solved : Wednesday, February 05, 2025 at 03:18:16 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

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

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

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