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I'm selling these fine leather jackets
Differential equations for the fail!
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<sup>t</sup>
Homogenous:
(a<sup>2</sup> - 2a + 5) e<sup>at</sup> = 0
a<sup>2</sup> - 2a + 5 = 0
D = (-2)<sup>2</sup> - 4 * 5 * 1 = -16
a = (2 +/- 4i) / 2 = 1 +/- 2i
x(t) = Ae<sup>(1+2i)t</sub> + Be<sub>(1-2i)t</sub>
Re(x(t)): e<sup>(1+2i)t</sup> = e<sup>t</sup> * (cos(2t) - i sin(2t))
= e<sup>t</sup> * cos(2t) - i * e<sup>t</sup> sin(2t)
(1+2i)* = 1-2i
x(t) = Ae<sup>(1+2i)t</sup> + Be<sup>(1-2i)t </sup>
= Ae<sup>t</sup> * cos(2t) - Ai * e<sup>t</sup> sin(2t) + Be<sup>t</sup> * cos(2t) + Bi * e<sup>t</sup> sin(2t)
x(t) = (A+B)cos(2t) * e<sup>t</sup> + (B-A)i * sin(2t) * e<sup>t</sup>
Can someone help me out with the particular solution?
Last edited by Aerith's Knight; 11-13-2008 at 11:43 PM.
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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:
x<sup>2</sup>
:</>D!
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I'm selling these fine leather jackets
Better?
And no.
I was thinking 4t cos(t) - 4t sin(t)
Im gonna check it now.
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Nono, I was just showing off the tags xD
I'm not edjamucated enough to solve that S:
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I'm selling these fine leather jackets
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.
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