I was looking at the thread where this person list the methods for differential equations. In the exact equation part, he appears to integrate ln(y) with respect to x and obtain xln(y). How do you do this?

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- Feb 22nd 2011, 05:34 AMPlague01integrating ln(y) w.r.t x
I was looking at the thread where this person list the methods for differential equations. In the exact equation part, he appears to integrate ln(y) with respect to x and obtain xln(y). How do you do this?

- Feb 22nd 2011, 05:39 AMProve It
Since it is being integrated w.r.t. $\displaystyle \displaystyle x$, $\displaystyle \displaystyle \ln{y}$ is treated as a constant.

What's the integral of a constant? - Feb 22nd 2011, 05:59 AMPlague01
- Feb 22nd 2011, 06:21 AMDrSteve
That is implicit differentiation. If y is a function of x, then that is how you would take the derivative.

- Feb 22nd 2011, 06:24 AMProve It
In this case, you are treating integration as the opposite of PARTIAL differentiation...

- Feb 22nd 2011, 06:48 AMPlague01