   Chapter 17.1, Problem 9E

Chapter
Section
Textbook Problem

Solve the differential equation.9. y" – 4y' + 13y = 0

To determine

To solve: The differential equation of y4y+13y=0 .

Explanation

Formula used:

Write the expression for differential equation.

ay+by+cy=0 (1)

Write the expression for auxiliary equation.

ar2+br+c=0 (2)

Write the expression for the complex roots.

r=α±iβ (3)

Write the expression for general solution of ay+by+cy=0 with complex roots.

y=eαx(c1cosβx+c2sinβx) (4)

Here,

α is the real part of the root, and

β is the imaginary part of the root.

Write the expression to find the roots of quadratic equation.

r=b±b24ac2a (5)

Consider the differential equation as follows.

y4y+13y=0 (6)

Compare equation (1) and equation (6).

a=1b=4c=13

Find the auxiliary equation.

Substitute 1 for a , 4 for b and 13 for c in equation (2),

(1)r2+(4)r+(13)=0r24r+13=0

Find the roots of equation using equation (5)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Use the guidelines of this section to sketch the curve. y=x3+13

Single Variable Calculus: Early Transcendentals, Volume I

Find the point of intersection of the two straight lines having the equations y =34x + 6 and 3x 2y + 3 = 0.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Sketch the polar curve. 12. r = 3 + cos 3

Single Variable Calculus: Early Transcendentals

The appropriate option for the value of (123).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 