73.17.37 problem 37

Internal problem ID [15500]
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 : Monday, March 31, 2025 at 01:39:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)+36*y(x) = 6*sec(6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\ln \left (\sec \left (6 x \right )\right ) \cos \left (6 x \right )}{6}+\cos \left (6 x \right ) c_1 +\sin \left (6 x \right ) \left (x +c_2 \right ) \]

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

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

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

✓ Sympy. Time used: 0.279 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) + Derivative(y(x), (x, 2)) - 6/cos(6*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x\right ) \sin {\left (6 x \right )} + \left (C_{2} + \frac {\log {\left (\cos {\left (6 x \right )} \right )}}{6}\right ) \cos {\left (6 x \right )} \]