Simple ODE

Thread Starter

boks

Joined Oct 10, 2008
218
y'(t) - ay(t) = 0

What is the form of the solution? \(C \cdot e^{at}\)

?


I have this ODE:

\( T'(t) - (1 - \frac{n^2}{4})T(t) = 0\)

If I'm right, the solutions should be of the form

\(C \cdot e^{(1- \frac{n^2}{4})t}\)

My book, however, says


\(C \cdot e^ {1- \frac{n^2}{4}t}\)

Who's right?
 

blazedaces

Joined Jul 24, 2008
130
Assuming that n is a constant, you're correct. Your book probably forgot to indicate the proper notation is all. I wouldn't rely too heavily on your books. Your books make mistakes too. Trust yourself sometimes too...

-blazed
 

Thread Starter

boks

Joined Oct 10, 2008
218
Brilliant.

And how about the equation

y' = (y - x)^2

what's the form of the solution here?

I find it hard to determine the form of solution of differential equations.
 
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