1st and 2nd derivative Problem.

[Ted_Grendy]

Hi all

I was wondering if someone could shed some light on the following question:

Given y = 2*x*e^(-3x)

Show that

d^2y/dx^2 + 6*dy/dx + 9y = 0

I have interpreted the question as the second derivative of the function + 6 times the first derivative of the function plus 9y is 0.

I know how to take the 1st and 2nd derivative.
I then multiply the 1st derivative by 6.

That's as far as I get.

Can anyone help?

Thanks

 

[Deleted member 4993]

Hi all

I was wondering if someone could shed some light on the following question:

Given y = 2*x*e^(-3x)

Show that

d^2y/dx^2 + 6*dy/dx + 9y = 0

I have interpreted the question as the second derivative of the function + 6 times the first derivative of the function plus 9y is 0.

I know how to take the 1st and 2nd derivative.
I then multiply the 1st derivative by 6.

That's as far as I get.

Can anyone help?

Thanks

I'll do a similar but different problem:

Given y = A * cos(w*x) .....Show that.........d^2y/dx^2 + w^2 * y = 0

y = A * cos(w*x)

y' = - A * w * sin(w*x)

y" = - A * w^2 * cos(w*x)

Now using the given differential equation:

d^2y/dx^2 + w^2 * y

= [- A * w^2 * cos(w*x)] + [w^2 * A * cos(w*x)]

= 0

follow the same path for your given problem

 

[Ted_Grendy]

Thanks

I'll do a similar but different problem:

Given y = A * cos(w*x) .....Show that.........d^2y/dx^2 + w^2 * y = 0

y = A * cos(w*x)

y' = - A * w * sin(w*x)

y" = - A * w^2 * cos(w*x)

Now using the given differential equation:

d^2y/dx^2 + w^2 * y

= [- A * w^2 * cos(w*x)] + [w^2 * A * cos(w*x)]

= 0

follow the same path for your given problem

I followed you process and I got 0.

Thank you.

 

[Steven G]

Hi all

I was wondering if someone could shed some light on the following question:

Given y = 2*x*e^(-3x)

Show that

d^2y/dx^2 + 6*dy/dx + 9y = 0

I have interpreted the question as the second derivative of the function + 6 times the first derivative of the function plus 9y is 0.

I know how to take the 1st and 2nd derivative.
I then multiply the 1st derivative by 6.

That's as far as I get.

Can anyone help?

Thanks

Hi, so why not do what YOU said, namely second derivative of the function + 6 times the first derivative of the function plus 9y is 0?? You said that you know how to take the 1st and 2nd derivatives and that you multiply the 1st derivative by 6. Now simple add 6dy/dx to d^2y/dx^2 and then add on 9y and verify that you get 0.

Please show us your work.