Question

solve the differential equation:
\[\frac{dx}{dt}=k(x-a)e^{-\frac {(x-a)^2}{b}}.\]

Answer 1

anyone ??

Answer 2

wt do we have to do?

Answer 3

that looks a lot like the normal distribution function

Answer 4

yes exactly @dumbcow....@doncatch you have to solve the differential equation and express x interms of t

Answer 5

This is a separable DE.
\[\frac{dx}{dt}=k(x-a)e^{-\frac {(x-a)^2}{b}} \implies \frac{dx}{k(x-a)}e^{\frac {(x-a)^2}{b}}=dt.\]
Integrate both sides now.

Answer 6

You probably know that the integral on the LHS can't be found in terms of elementary functions. So you can write
\[\large \int_0^x \frac{e^{\frac {(\lambda-a)^2}{b}}}{{k(\lambda-a)}} d\lambda=t+c.\]