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# Differential equation - Help me please :) watch

1. I started by trying to find the auxillary equation, as this is a homogenous second order DE.

I get to this:

k^2 - 2k + 1 + E^2

What can I do from here? (k-1)(k-1) + E^2 ???
2. Set the quadratic equal to 0 and solve for k. E^2 is just a constant.
3. (Original post by Daniel Freedman)
Set the quadratic equal to 0 and solve for k. E^2 is just a constant.
That's what I don't quite understand ..

You gwt k^2 -2k +(1+E^2) = 0

How do you factorise that?!
4. (Original post by Cggh90)
That's what I don't quite understand ..

You gwt k^2 -2k +(1+E^2) = 0

How do you factorise that?!
You don't need to factorise it necessarily.

Continuing from where you left off,

.

You could have just used the quadratic formula from the start instead of completing the square, but both are fine.
5. (Original post by Daniel Freedman)
You don't need to factorise it necessarily.

Continuing from where you left off,

.

You could have just used the quadratic formula from the start instead of completing the square, but both are fine.
Hmm, that kind of makes sense but still a bit confused.. First isn't it k = -1 rather than + 1?

Why does the imaginary number come into this?

I'm guessing the next bit is that y = e^x(A cos E x + B sin E x) ???

6. Square rooting both sides generates the i.

And you're correct about the next bit.
7. (Original post by Daniel Freedman)

Square rooting both sides generates the i.

And you're correct about the next bit.
I'm still finding it hard! :L

For th next part, I am trying to find the general solution

y=e^x(A cosE x + B sin E x)

x=0 at y=1

So 1 = 1(AcosE) ?

The constant, E, is confusing me with this part !
8. You have .

When you plug in x = 0, you have

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