28.2.12 problem 12

Internal problem ID [4455]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 12
Date solved : Monday, January 27, 2025 at 09:17:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-64 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$6)-64*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\left ({\mathrm e}^{3 x} c_6 +c_4 \,{\mathrm e}^{x}\right ) \cos \left (\sqrt {3}\, x \right )+\left ({\mathrm e}^{3 x} c_5 +c_3 \,{\mathrm e}^{x}\right ) \sin \left (\sqrt {3}\, x \right )+c_{2} {\mathrm e}^{4 x}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 68

DSolve[D[y[x],{x,6}]-64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_1 e^{4 x}+e^x \left (c_2 e^{2 x}+c_3\right ) \cos \left (\sqrt {3} x\right )+e^x \left (c_6 e^{2 x}+c_5\right ) \sin \left (\sqrt {3} x\right )+c_4\right ) \]