32.7.9 problem Exercise 20.10, page 220

Internal problem ID [5924]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.10, page 220
Date solved : Monday, January 27, 2025 at 01:27:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-a^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve(diff(y(x),x$4)-a^2*y(x)=0,y(x), singsol=all)
 

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

✓ 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]
 

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