80.8.5 problem 5

Internal problem ID [18584]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:03:00 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 53

DSolve[D[y[x],{x,4}]-a^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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