73.17.37 problem 37

Internal problem ID [15571]
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
Date solved : Tuesday, January 28, 2025 at 08:02:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+36 y&=6 \sec \left (6 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)+36*y(x)=6*sec(6*x),y(x), singsol=all)
 

\[ y = -\frac {\ln \left (\sec \left (6 x \right )\right ) \cos \left (6 x \right )}{6}+c_{1} \cos \left (6 x \right )+\sin \left (6 x \right ) \left (x +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]+36*y[x]==6*Sec[6*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x+c_2) \sin (6 x)+\cos (6 x) \left (\frac {1}{6} \log (\cos (6 x))+c_1\right ) \]