73.16.21 problem 24.4 (c)

Internal problem ID [15533]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.4 (c)
Date solved : Tuesday, January 28, 2025 at 08:01:25 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-81 y&=\sinh \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 53

dsolve(diff(y(x),x$4)-81*y(x)=sinh(x),y(x), singsol=all)
 

\[ y = \frac {\left (160 c_{3} {\mathrm e}^{6 x}+160 c_4 \sin \left (3 x \right ) {\mathrm e}^{3 x}+160 \cos \left (3 x \right ) c_{1} {\mathrm e}^{3 x}-{\mathrm e}^{4 x}+{\mathrm e}^{2 x}+160 c_{2} \right ) {\mathrm e}^{-3 x}}{160} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 100

DSolve[D[y[x],{x,4}]-81*y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (3 x) \int _1^x\frac {1}{54} \sin (3 K[1]) \sinh (K[1])dK[1]+\sin (3 x) \int _1^x-\frac {1}{54} \cos (3 K[2]) \sinh (K[2])dK[2]+\frac {e^{-x}}{288}-\frac {e^x}{288}+c_1 e^{3 x}+c_3 e^{-3 x}+c_2 \cos (3 x)+c_4 \sin (3 x) \]