73.16.3 problem 24.1 (c)

Internal problem ID [15444]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (c)
Date solved : Monday, March 31, 2025 at 01:37:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

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

\[ y = -\frac {\ln \left (\csc \left (2 x \right )\right ) \sin \left (2 x \right )}{4}+\frac {\left (-2 x +4 c_1 \right ) \cos \left (2 x \right )}{4}+\sin \left (2 x \right ) c_2 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.322 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + Derivative(y(x), (x, 2)) - 1/sin(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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