20.7.16 problem Problem 41

Internal problem ID [3731]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 41
Date solved : Sunday, March 30, 2025 at 02:06:45 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }&=5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 58

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+104*diff(diff(diff(y(x),x),x),x)+2740*diff(diff(y(x),x),x) = 5*exp(-2*x)*cos(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\left (667 c_1 +156 c_2 \right ) \cos \left (6 x \right )-156 \sin \left (6 x \right ) \left (c_1 -\frac {667 c_2}{156}\right )\right ) {\mathrm e}^{-52 x}}{1876900}+\frac {5 \left (-695 \cos \left (3 x \right )-2448 \sin \left (3 x \right )\right ) {\mathrm e}^{-2 x}}{84184477}+c_3 x +c_4 \]

✓ Mathematica. Time used: 2.781 (sec). Leaf size: 82

ode=D[y[x],{x,4}]+104*D[y[x],{x,3}]+2740*D[y[x],{x,2}]==5*Exp[-2*x]*Cos[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {12240 e^{-2 x} \sin (3 x)}{84184477}-\frac {3475 e^{-2 x} \cos (3 x)}{84184477}+c_4 x+\frac {(156 c_1+667 c_2) e^{-52 x} \cos (6 x)}{1876900}+\frac {(667 c_1-156 c_2) e^{-52 x} \sin (6 x)}{1876900}+c_3 \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2740*Derivative(y(x), (x, 2)) + 104*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) - 5*exp(-2*x)*cos(3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + \left (C_{3} \sin {\left (6 x \right )} + C_{4} \cos {\left (6 x \right )}\right ) e^{- 52 x} - \frac {12240 e^{- 2 x} \sin {\left (3 x \right )}}{84184477} - \frac {3475 e^{- 2 x} \cos {\left (3 x \right )}}{84184477} \]