68.1.4 problem Problem 1.3(b)

Internal problem ID [14054]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS. Problems page 28
Problem number : Problem 1.3(b)
Date solved : Wednesday, March 05, 2025 at 10:27:39 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

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

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.282 (sec). Leaf size: 26

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

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