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1. c4 formation of differential equations question help
Here's the question:
the variables x and t are such that the rate of increase of lnx with respect to t is proportional to x.
a) express this statement as an equation, and hence show that the rate of increase of x with respect to t is proportional to x^2.

I got that dlnx/dt = kx

but how do you do show dx/dt =kx^2?

thanks
2. Re: c4 formation of differential equations question help
Differentiate lnx with respect to t.

I.e d(lnx)/dt
3. Re: c4 formation of differential equations question help
Differentiate lnx with respect to t.

I.e d(lnx)/dt

How would you do that?
4. Re: c4 formation of differential equations question help
It should be in a formula packet, if not memorized.

lnx=t
x=e^t

dx/dt=e^t, t=lnx
dt/dx=...
5. Re: c4 formation of differential equations question help
(Original post by ejwm)
How would you do that?

6. Re: c4 formation of differential equations question help
(Original post by ejwm)
Here's the question:
the variables x and t are such that the rate of increase of lnx with respect to t is proportional to x.
a) express this statement as an equation, and hence show that the rate of increase of x with respect to t is proportional to x^2.

I got that dlnx/dt = kx

but how do you do show dx/dt =kx^2?

thanks
You have d/dt lnx = kx and d/dx lnx = 1/x, so combining these...
7. Re: c4 formation of differential equations question help