44.1.56 problem 71

Internal problem ID [6931]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 71
Date solved : Wednesday, March 05, 2025 at 02:52:56 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-20*diff(diff(diff(y(x),x),x),x)+158*diff(diff(y(x),x),x)-580*diff(y(x),x)+841*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 36

ode=D[y[x],{x,4}]-20*D[y[x],{x,3}]+158*D[y[x],{x,2}]-580*D[y[x],x]+841*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.268 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(841*y(x) - 580*Derivative(y(x), x) + 158*Derivative(y(x), (x, 2)) - 20*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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