28.2.38 problem 38

Internal problem ID [4481]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 38
Date solved : Sunday, March 30, 2025 at 03:23:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.091 (sec). Leaf size: 17

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

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