28.2.43 problem 43

Internal problem ID [4486]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 43
Date solved : Sunday, March 30, 2025 at 03:23:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (x \right )+10 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+2*y(x) = 5*cos(x)+10*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \sin \left (x \right ) c_2 +{\mathrm e}^{-x} \cos \left (x \right ) c_1 +\cos \left (x \right )+2 \sin \left (x \right )-\sin \left (2 x \right )-2 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.312 (sec). Leaf size: 42

ode=D[y[x],{x,2}]+2*D[y[x],x]+2*y[x]==5*Cos[x]+10*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 \cos (2 x)+\left (2+c_1 e^{-x}\right ) \sin (x)+\cos (x) \left (-2 \sin (x)+c_2 e^{-x}+1\right ) \]

✓ Sympy. Time used: 0.227 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 10*sin(2*x) - 5*cos(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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