89.20.4 problem 4

Internal problem ID [24760]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Oral Exercises at page 154
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:47:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to \left (\frac {1}{16}+c_1\right ) \cos (2 x)+\frac {1}{4} (x+4 c_2) \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 19

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

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