Match the following differential equation

y''+ 7y'+ 12y= 0

with its correct solution:

1. y = x^(1/2)

2. y = e^(-4x)

3. y = sin(x)

4. y = 3x + x^2

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You can solve this by taking the first and second derivatives of each of the possible solutions, and then plugging them into the differential equation to see if you really get 0. The answer turns out to be the second function:

`y=e^(-4x)`

`y'=-4e^(-4x)`

`y''=16 e^(-4x)`

Plugging these into the differential equation, we have:

`16e^(-4x) + 7(-4)e^(-4x)+12e^(-4x) = 0`

That is, this really does solve your ode.

Thus the correct solution is #2

 

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial