First order linear differential equation

[physicsernaw]

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 = P⁰e^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)

:)

 

[CompuChip]

Well done! :)