15.11.25 problem 25

Internal problem ID [3135]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 25
Date solved : Sunday, March 30, 2025 at 01:19:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=8 \sin \left (x \right )^{2} \end{align*}

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

ode:=diff(diff(y(x),x),x)+4*y(x) = 8*sin(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 -1\right ) \cos \left (2 x \right )+1+\left (c_2 -x \right ) \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 27

ode=D[y[x],{x,2}]+4*y[x]==8*Sin[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (-1+c_1) \cos (2 x)+(-x+c_2) \sin (2 x)+1 \]

✓ Sympy. Time used: 0.642 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 8*sin(x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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