Question

Would love some help with a derivatives question please

Answer 1

find the general solution of the following system of equations:
dx/dt = 2y - 4x
dy/dt = 2y - (5/2)x

Answer 2

I've never done anything like this with derivatives, but i'm going to go out on a limb and treat it like any other system of equations:
\[\frac{ dx }{ dt } = 2y - 4x\]\[\frac{ dy }{ dt } = 2y - \frac{ 5 }{ 2 }x\]
\[2y = \frac{ dy }{ dt }+\frac{ 5 }{ 2 }x\]
Substituting back into the first equation:
\[\frac{ dx }{ dt } = \frac{ dy }{ dt }+\frac{ 5 }{ 2 }x - \frac{ 8 }{ 2 }x = \frac{ dy }{ dt } - \frac{ 3 }{ 2 }x\]Now just taking the antiderivative of this? (I don't really know what i'm doing, lol.)

Answer 3

I dunno, I give up. I'm really just spitting numbers. And it's probably wrong.

Answer 4

...yeah i dont think i can just do the anti-derivative give that one's the derivative of x and the other's the derivative of y... but not sure, i'm lost too hey

Answer 5

You could sort of and treat it in the same way you treat implicit differentiation, but again, that's like a "what if" on top of a "what if" on top of a "what if", lol. My advice is to cry yourself to sleep not knowing the answer to the tune of http://www.youtube.com/watch?v=45x91IM5-A4

Answer 6

(Only the scary part, of course.)

Answer 7

lol

Answer 8

@Mertsj @jim_thompson5910 *Calls in the heavy artillery*

Answer 9

@hartnn think this guys great too

Answer 10

Maybe you could eliminate the parameter dt

Answer 11

ok... but how?

Answer 12

i would understand how if it was dx/dy or dy/dx... but it's dt

Answer 13

Please bump this if you don't figure it out yourself, i'd really like to know how to do this, too. And if you find an answer, please share it with me :E

Answer 14

will do man

Answer 15

I got a suggestion from my friend: Divide dy/dt by dx/dt to get dy/dx and then find the simplest antiderivative with respect to x.