50.14.21 problem 3(e)

Internal problem ID [8059]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 3(e)
Date solved : Wednesday, March 05, 2025 at 05:27:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sec \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 81

ode:=diff(diff(y(x),x),x)+9*y(x) = sec(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {2}{3}+\frac {\left (-4 \cos \left (x \right )^{3}+3 \cos \left (x \right )\right ) \sqrt {2}\, \operatorname {arctanh}\left (\cos \left (x \right ) \sqrt {2}\right )}{6}+\frac {\sin \left (x \right ) \left (-4 \cos \left (x \right )^{2}+1\right ) \sqrt {2}\, \operatorname {arctanh}\left (\sin \left (x \right ) \sqrt {2}\right )}{6}+4 c_{1} \cos \left (x \right )^{3}+\frac {4 \left (3 \sin \left (x \right ) c_{2} +1\right ) \cos \left (x \right )^{2}}{3}-3 \cos \left (x \right ) c_{1} -\sin \left (x \right ) c_{2} \]

✓ Mathematica. Time used: 0.203 (sec). Leaf size: 102

ode=D[y[x],{x,2}]+9*y[x]==Sec[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{6} \left (-\sqrt {2} \sin (3 x) \text {arctanh}\left (\sqrt {2} \sin (x)\right )-\sqrt {2} \cos (3 x) \text {arctanh}\left (\sqrt {2}-\tan \left (\frac {x}{2}\right )\right )-\sqrt {2} \cos (3 x) \text {arctanh}\left (\tan \left (\frac {x}{2}\right )+\sqrt {2}\right )+4 \cos (2 x)+6 c_1 \cos (3 x)+6 c_2 \sin (3 x)\right ) \]

✓ Sympy. Time used: 13.922 (sec). Leaf size: 600

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + Derivative(y(x), (x, 2)) - 1/cos(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]