Differential equations for the fail!

[Aerith's Knight]

Ok, I have an exam tomorrow, and I was just practising, and I can't get this freaking differential equation. >:[

This is what I have so far:

x''(t) -2x'(t) + 5x(t) = 4t * e^t

Homogenous:

(a² - 2a + 5) e^at = 0

a² - 2a + 5 = 0
D = (-2)² - 4 * 5 * 1 = -16

a = (2 +/- 4i) / 2 = 1 +/- 2i

x(t) = Ae<sup>(1+2i)t</sub> + Be_(1-2i)t

Re(x(t)): e^(1+2i)t = e^t * (cos(2t) - i sin(2t))
= e^t * cos(2t) - i * e^t sin(2t)

(1+2i)* = 1-2i

x(t) = Ae^(1+2i)t + Be^(1-2i)t
= Ae^t * cos(2t) - Ai * e^t sin(2t) + Be^t * cos(2t) + Bi * e^t sin(2t)

x(t) = (A+B)cos(2t) * e^t + (B-A)i * sin(2t) * e^t

Can someone help me out with the particular solution?

[Jessweeee♪]

Here's a tip: <</>sup><</>/sup> will make super script, which is good for typing out exponents. It makes things a lot easier to read :kaodizzy:

x²


:</>D!

[Aerith's Knight]

Better?

And no.

I was thinking 4t cos(t) - 4t sin(t)

Im gonna check it now.

[Jessweeee♪]

Nono, I was just showing off the tags xD


I'm not edjamucated enough to solve that S:

[Aerith's Knight]

I've got it.

x(t) = 0.8t cos(t) + 0.4t sin(t)

I think I get it now. If a mod sees this, you can close the thread.