32.7.21 problem Exercise 20.22, page 220

Internal problem ID [5936]
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 20.22, page 220
Date solved : Monday, January 27, 2025 at 01:27:44 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 48

dsolve(diff(y(x),x$4)-8*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{\sqrt {5}\, x} \sin \left (x \right )-c_{2} {\mathrm e}^{-\sqrt {5}\, x} \sin \left (x \right )+c_3 \,{\mathrm e}^{\sqrt {5}\, x} \cos \left (x \right )+c_4 \,{\mathrm e}^{-\sqrt {5}\, x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 142

DSolve[D[y[x],{x,4}]-8*D[y[x],{x,2}]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\sqrt {6} x \cos \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )} \left (\left (c_3 e^{2 \sqrt {6} x \cos \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )}+c_2\right ) \cos \left (\sqrt {6} x \sin \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )\right )+\sin \left (\sqrt {6} x \sin \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )\right ) \left (c_1 e^{2 \sqrt {6} x \cos \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )}+c_4\right )\right ) \]