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## Homework Statement

dy/dt = k*y*ln(y/M), where M and k are constants.

Show that y = Me

^{aekt}satisfies the above equation for any constant a.

## Homework Equations

y' = ky

y = P

^{0}e

^{kt}

## The Attempt at a Solution

Taking the derivative of y, I get:

(Me

^{aekt})*(ae

^{kt})*k

which is,

ky*ae

^{kt}

..and I'm stuck here.

EDIT:

Nevermind, I figured it out.

ln(y) = ln(M) + ae^(kt)

ae^(kt) = ln(y/M)

Plugging back in...

ky*ln(y/M)

:)

Last edited: