Internal problem ID [13835]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+36 y=6 \sec \left (6 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+36*y(x)=6*sec(6*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\ln \left (\sec \left (6 x \right )\right ) \cos \left (6 x \right )}{6}+\cos \left (6 x \right ) c_{1} +\sin \left (6 x \right ) \left (c_{2} +x \right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 32
DSolve[y''[x]+36*y[x]==6*Sec[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x+c_2) \sin (6 x)+\cos (6 x) \left (\frac {1}{6} \log (\cos (6 x))+c_1\right ) \]