20.9.3 problem Problem 3

Internal problem ID [3747]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 3
Date solved : Monday, January 27, 2025 at 07:58:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=18 \sec \left (3 x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+9*y(x)=18*sec(3*x)^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{1} -2\right ) \cos \left (3 x \right )+\sin \left (3 x \right ) c_{2} +\sec \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.095 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]+9*y[x]==18*Sec[3*x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \sec (3 x) ((-2+c_1) \cos (6 x)+c_2 \sin (6 x)+c_1) \]