50.14.24 problem 3(h)

Internal problem ID [8062]
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(h)
Date solved : Sunday, March 30, 2025 at 12:41:52 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\tan \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

ode:=diff(diff(y(x),x),x)+4*y(x) = tan(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-1+2 \cos \left (x \right )^{2}\right ) \ln \left (\cos \left (x \right )\right )+2 c_1 \cos \left (x \right )^{2}+2 \sin \left (x \right ) \left (x +c_2 \right ) \cos \left (x \right )-\frac {3 \sin \left (x \right )^{2}}{2}-c_1 \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 32

ode=D[y[x],{x,2}]+4*y[x]==Tan[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (x+c_2) \sin (2 x)+\cos (2 x) \left (\log (\cos (x))+\frac {1}{4}+c_1\right )-\frac {3}{4} \]

✓ Sympy. Time used: 1.150 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - tan(x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \log {\left (\cos {\left (x \right )} \right )}\right ) \cos {\left (2 x \right )} + \left (C_{2} + x - \frac {\tan {\left (x \right )}}{2}\right ) \sin {\left (2 x \right )} - \frac {1}{4} \]