28.2.29 problem 29

Internal problem ID [4472]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 29
Date solved : Tuesday, March 04, 2025 at 06:46:09 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 58

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*diff(diff(y(x),x),x)-y(x) = 44*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \sin \left (3 x \right )+c_4 \,{\mathrm e}^{-\sqrt {\sqrt {5}-2}\, x}+c_{2} {\mathrm e}^{\sqrt {\sqrt {5}-2}\, x}+c_3 \sin \left (\sqrt {\sqrt {5}+2}\, x \right )+c_{1} \cos \left (\sqrt {\sqrt {5}+2}\, x \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 81

ode=D[y[x],{x,4}]+4*D[y[x],{x,2}]-y[x]==44*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sin (3 x)+c_3 e^{\sqrt {\sqrt {5}-2} x}+c_4 e^{-\sqrt {\sqrt {5}-2} x}+c_1 \cos \left (\sqrt {2+\sqrt {5}} x\right )+c_2 \sin \left (\sqrt {2+\sqrt {5}} x\right ) \]

✓ Sympy. Time used: 0.159 (sec). Leaf size: 68

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 44*sin(3*x) + 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x \sqrt {-2 + \sqrt {5}}} + C_{2} e^{x \sqrt {-2 + \sqrt {5}}} + C_{3} \sin {\left (x \sqrt {2 + \sqrt {5}} \right )} + C_{4} \cos {\left (x \sqrt {2 + \sqrt {5}} \right )} + \sin {\left (3 x \right )} \]