Internal problem ID [2267]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-18 \left (\sec ^{3}\left (3 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+9*y(x)=18*sec(3*x)^3,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}+\frac {-2 \left (\cos ^{2}\left (3 x \right )\right )+1}{\cos \left (3 x \right )} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 32
DSolve[y''[x]+9*y[x]==18*Sec[3*x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sec (3 x) ((-2+c_1) \cos (6 x)+c_2 \sin (6 x)+c_1) \\ \end{align*}