Internal problem ID [2271]
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 7.
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-\frac {36}{4-\left (\cos ^{2}\left (3 x \right )\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 59
dsolve(diff(y(x),x$2)+9*y(x)=36/(4-cos(3*x)^2),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}+\frac {4 \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \sin \left (3 x \right )}{3}\right ) \sin \left (3 x \right )}{3}-\left (-\ln \left (\cos \left (3 x \right )+2\right )+\ln \left (\cos \left (3 x \right )-2\right )\right ) \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 52
DSolve[y''[x]+9*y[x]==36/(4-Cos[3*x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sin (3 x)+\frac {4 \sin (3 x) \cot ^{-1}\left (\sqrt {3} \csc (3 x)\right )}{\sqrt {3}}+\cos (3 x) \left (2 \coth ^{-1}(2 \sec (3 x))+c_1\right ) \\ \end{align*}