Answer: In each of 7 through 12, find the solution of the given initial value problem

Chapter 3, Problem 7

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

In each of 7 through 12, find the solution of the given initial value problem. Sketch the graph of the solution and describe its behavior as t increases. y__ + y_ 2y = 0, y(0) = 1, y_(0) = 1 G

Questions & Answers

QUESTION:

In each of 7 through 12, find the solution of the given initial value problem. Sketch the graph of the solution and describe its behavior as t increases. y__ + y_ 2y = 0, y(0) = 1, y_(0) = 1 G

ANSWER:

Step 1 of 4

The objective is to find the general solution for the following initial value problem:

,

Assume that is a solution of the homogeneous equation.

Find the first and second derivative of the function.

Substitute the values, , and in .

                                             

Since, then

Thus, the characteristic equation for the differential equation is.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back