Consider the following second-order differential equation with constant coefficients, d² - z (x) − 8 ( d z(x)) + 16 z (x) = 0 dz2 (a) By seeking solutions of the form z(x) = ePa, determine the characteristic equation in terms of p (rather than the usual X). Enter the characteristic equation below, including the equals sign, "=". exp(p*x)-8*exp(p*x)+16*exp (b) What are the roots of the characteristic equation? Enter in the form P₁, P2. & P (c) What is the general solution of this differential equation? Note: You must use capital A and capital B as your constants of integration. z(x) = & P (d) Solve the initial value problem consisting of the differential equation above together with initial conditions z (0) = -5, z (0) = 7, and enter your solution for z (a) below.
Consider the following second-order differential equation with constant coefficients, d² - z (x) − 8 ( d z(x)) + 16 z (x) = 0 dz2 (a) By seeking solutions of the form z(x) = ePa, determine the characteristic equation in terms of p (rather than the usual X). Enter the characteristic equation below, including the equals sign, "=". exp(p*x)-8*exp(p*x)+16*exp (b) What are the roots of the characteristic equation? Enter in the form P₁, P2. & P (c) What is the general solution of this differential equation? Note: You must use capital A and capital B as your constants of integration. z(x) = & P (d) Solve the initial value problem consisting of the differential equation above together with initial conditions z (0) = -5, z (0) = 7, and enter your solution for z (a) below.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Consider the following second-order differential equation with constant coefficients,
d²
- z (x) − 8 ( d z(x)) + 16 z (x) = 0
dz2
(a) By seeking solutions of the form z(x) = ePa, determine the characteristic equation in terms of p (rather than the usual X).
Enter the characteristic equation below, including the equals sign, "=".
exp(p*x)-8*exp(p*x)+16*exp
(b) What are the roots of the characteristic equation? Enter in the form P₁, P2.
& P
(c) What is the general solution of this differential equation?
Note: You must use capital A and capital B as your constants of integration.
z (x) =
& P
(d) Solve the initial value problem consisting of the differential equation above together with initial conditions z (0) = -5, z (0) = 7, and enter your solution
for z (a) below.
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