How would I use separation of variable to find the general solution to this differential equation? I don't really even know where to start.

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- September 15th 2009, 10:27 PMdrew.walkerSeparation of variables to solve growth equation
How would I use separation of variable to find the general solution to this differential equation? I don't really even know where to start.

- September 15th 2009, 10:56 PMchisigma
Generally specking if we wtite the equation as...

(1)

... we can separate the variables sterting from (1) in such way...

(2)

... where is an 'arbitrary constant'...

Kind regards

- September 15th 2009, 11:06 PMdrew.walker
Now I'm really confused. :)

Where did a(t) come from? Or are you just speaking generally? Should I be assigning aspects of the equation to those variables? e.g:

Any extra help would be greatly appreciated. I really can't seem to grasp the separation of variable method. Do you know of any good examples that step through working? - September 15th 2009, 11:22 PMdrew.walker
Ah, I think I just had an epiphany thanks to Midnight Tutor (MidnightTutor.com Free Online Calculus and Chemistry Tutorials).

Is this the general solution? or does it need to be taken somewhere from there? - September 15th 2009, 11:42 PMchisigma
Setting and applying the procedure I have indicated you arrive to write...

(1)

... where c>0 is an arbitrary constant. Exponentiating both terms of (1) you obtain...

(2)

That's the general solution!...

Kind regards

- September 15th 2009, 11:47 PMdrew.walker
Ah, okay. Now I'm starting to get it. Thanks for the help.