First order linear differential equation

  • #1

Homework Statement



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

Show that y = Meaekt satisfies the above equation for any constant a.

Homework Equations



y' = ky
y = P0ekt

The Attempt at a Solution



Taking the derivative of y, I get:

(Meaekt)*(aekt)*k

which is,

ky*aekt

..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:

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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Well done! :)
 

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