15.12.6 problem 6

Internal problem ID [3150]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 6
Date solved : Tuesday, March 04, 2025 at 04:03:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \frac {\left (x +2 c_{1} \right ) \cos \left (2 x \right )}{2}+\sin \left (2 x \right ) c_2 +\frac {x}{2} \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.104 (sec). Leaf size: 22

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

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