Okay I have a problem with using variables in differential equations

1. Jul 7, 2012

klovely

Consider the differential equation
where I''+I=e^it where i= sqrt (-1)

So I don't know what to do. I do know that The second derivative of
c*t*e^(i*t) is
-c e^(i t) (-2 i+t)
But I don't know what to do for a and b and I need help to get threw this problem before I take my test.

a) Find c such that I(t)=cte^it is a solution.

Is the equation given what the problem is differentiated? then would you just solve for c?

b) Find the general solution and discuss what happens as t approaches infinity .

How would you incorporate an infinity?

2. Jul 7, 2012

Simon Bridge

Yep - you put that relation into the differential equation so every time you see an I you put that and every time you see I'' you put the second derivative and so on, then solve for c.
It's not going to look obvious that it will work out before you begin - you just have to write it down and then figure it out.

Hint: use limits.

Last edited: Jul 7, 2012
3. Jul 7, 2012

klovely

Thank you soooo much!