84.26.3 problem 15.8

Internal problem ID [22270]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 15. Variation of parameteres. Supplementary problems
Problem number : 15.8
Date solved : Thursday, October 02, 2025 at 08:36:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_1 +\frac {1}{8}+\frac {\cos \left (4 x \right )}{24} \]

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to \frac {1}{24} \cos (4 x)+c_1 \cos (2 x)+c_2 \sin (2 x)+\frac {1}{8} \end{align*}

✓ Sympy. Time used: 0.259 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )} + \frac {\sin ^{4}{\left (x \right )}}{3} - \frac {\sin ^{2}{\left (x \right )}}{3} + \frac {1}{6} \]