 7
 0
The question is attached. Thanks a lot
Attachments

20.3 KB Views: 346
So what do we do with this?Okay, so now you know the value of F(0)!
The problem SAID "Write a differential equation for F(x):So what do we do with this?
Sorry, im not understanding.
The problem SAID "Write a differential equation for F(x):
[tex]\frac{dF}{d\omega}+ h(\omega)F[/tex]
with F(0)= F0 where F0 is the constant you have to determine explicitly."
Okay, you now know that F0= [itex]\sqrt{\pi}[/itex].
By the way, I notice that the "differential equation" you give (I have copied it exactly above) is not an equation! There is no equal sign. I imagine it is actually either
[tex]\frac{dF}{d\omega}= h(\omega)F[/tex]
or
[tex]\frac{dF}{d\omega}+ h(\omega)F= 0[/tex]
They differ, of course, only in the sign of h.
Apparently you are having trouble reading the problem which I just quoted.Oh so we just have to solve the ODE [tex]\frac{dF}{d\omega}+ h(\omega)F= 0[/tex] with initial condition F0= [itex]\sqrt{\pi}[/itex]...
is it that straight forward? Am I not understanding something?
I applogize, it's not every day I come accross questions like this...this is very challenging.This is becoming very frustrating. Is there any point in responding if you don't read the replies?? I just said, the problem does not ask you to solve a differential equation, it asks you to find a differential equation for F! And I don't know what you mean by "the answer to this integral". Integrals don't have answers, questions do. What is the question?
You are told that F is defined by
[tex]F(\omega)= \int_{\infty}^{\infty}e^{\omega x}e^{x^2}dx[/tex]
What do you get if you differentiate that equation with respect to [itex]\omega[/itex]? (In this case it is legitimate to simplydifferentiate inside the integral.)
By the way, [tex]e^{i\omega x}e^{x^2}= e^{i\omega x x^2}[/tex]