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]]
\[ \boxed {y^{\prime \prime }+9 y=2 \sec \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+9*y(x)=2*sec(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \ln \left (\sec \left (3 x \right )\right ) \cos \left (3 x \right )}{9}+\cos \left (3 x \right ) c_{1} +\frac {2 \sin \left (3 x \right ) \left (x +\frac {3 c_{2}}{2}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 39
DSolve[y''[x]+9*y[x]==2*Sec[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} (2 x+3 c_2) \sin (3 x)+\cos (3 x) \left (\frac {2}{9} \log (\cos (3 x))+c_1\right ) \]