49.9.3 problem 1(c)

Internal problem ID [7652]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 83
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:09:04 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

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

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

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