12.18.31 problem section 9.2, problem 43(d)

Internal problem ID [2145]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 43(d)
Date solved : Monday, January 27, 2025 at 05:42:48 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 78

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

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