49.7.1 problem 4(a)

Internal problem ID [7640]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(a)
Date solved : Monday, January 27, 2025 at 03:08:54 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)-8*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_3 \,{\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_1 e^{3 x}+c_2 \cos \left (\sqrt {3} x\right )+c_3 \sin \left (\sqrt {3} x\right )\right ) \]