Internal problem ID [248]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 53.
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-2 \sec \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+9*y(x)=2*sec(3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}+\frac {2 \sin \left (3 x \right ) x}{3}-\frac {2 \ln \left (\frac {1}{\cos \left (3 x \right )}\right ) \cos \left (3 x \right )}{9} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 39
DSolve[y''[x]+9*y[x]==2*Sec[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} (2 x+3 c_2) \sin (3 x)+\cos (3 x) \left (\frac {2}{9} \log (\cos (3 x))+c_1\right ) \\ \end{align*}