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FP3 Differential Equations Help

Triso

Reply 1

ghostwalker

Original post by Triso

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I refer you to the posting guidelines

Reply 2

Triso

I suppose I wasn't clear. I've completed the first part of the question finding the differential equation connecting x and t; the equation being dx/dt=c(a +bsincx - y). However I don't know where to start with the second part of the question, showing what x is equal to.

Reply 3

Triso

I would like some guidance as to how complete/start working out the part of the question, "show that , after some time, x is approximately equal to..." please.

Reply 4

ghostwalker

Original post by Triso

I would like some guidance as to how complete/start working out the part of the question, "show that , after some time, x is approximately equal to..." please.

It's going to depend on what you got for the first part of the question - what was that?

Reply 5

Triso

Original post by ghostwalker

It's going to depend on what you got for the first part of the question - what was that?

the equation I got relating x and t was dx/dt=c(a +bsincx - y)

Reply 6

ghostwalker

Original post by Triso

the equation I got relating x and t was dx/dt=c(a +bsincx - y)

I make it:

\displaystyle \frac{dx}{dt}=c(a+b\sin (ct)-x)

Rearranging to:

\displaystyle \frac{dx}{dt}+cx= ac+bc\sin (ct)

So we need to start by getting a solution to that d.e.

For large values of t, the complementary function will tend to zero, and we're left with the particular integral which should tend to the desired function, if not actually being that.