49.7.2 problem 4(b)

Internal problem ID [7641]
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(b)
Date solved : Monday, January 27, 2025 at 03:08:54 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 65

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 67

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

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