73.12.26 problem 19.4 (j)

Internal problem ID [15378]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.4 (j)
Date solved : Tuesday, January 28, 2025 at 07:53:54 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

dsolve(diff(y(x),x$6)+16*diff(y(x),x$3)+64*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 60

DSolve[D[y[x],{x,6}]+16*D[y[x],{x,3}]+64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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