Integration - Correct?

**jokke22** · May 20th 2009, 06:54 AM

Hi!

I have been given an equation:
$\frac{dy}{dt}=\lambda y$

Which by integration I find to be:

$\int \frac{dy}{dt}dt = \int \lambda y dt \rightarrow lny+c = \int \lambda dt = \lambda t+C2$

Is this correct?

**Danny** · May 20th 2009, 07:17 AM

Originally Posted by jokke22

Hi!

I have been given an equation:
$\frac{dy}{dt}=\lambda y$

Which by integration I find to be:

$\int \frac{dy}{dt}dt = \int \lambda y dt \rightarrow lny+c = \int \lambda dt = \lambda t+C2$

Is this correct?

Yes but you can combine the two constants. Usually we write the solution as $y = ce^{\lambda t}$ .

**jokke22** · May 20th 2009, 07:38 AM

Aha! I didn't know they were the same at the point! Thanks danny!

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