71.10.10 problem 10

Internal problem ID [14505]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:42:43 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 47

dsolve(diff(y(x),x$8)+8*diff(y(x),x$4)+16*y(x)=0,y(x), singsol=all)
 

\[ y = \left (\left (c_4 x +c_{2} \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_{3} x +c_{1} \right )\right ) {\mathrm e}^{-x}+\left (\left (c_8 x +c_6 \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_7 x +c_5 \right )\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 66

DSolve[D[y[x],{x,8}]+8*D[y[x],{x,4}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (c_4 x+c_7 e^{2 x}+c_8 e^{2 x} x+c_3\right ) \cos (x)+\left (c_2 x+c_5 e^{2 x}+c_6 e^{2 x} x+c_1\right ) \sin (x)\right ) \]