Exponential martingale:

SDE and it's solution:

 One would try directly integrate Unknown macro: formula. Click on this message for details.
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But having Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator. in integral is problematic.Instead direct integration, we may recall that for non-stochastic function: Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.

With this idea let's define Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.and apply Ito lemma to this new process:

As you can see contrary to non-stochastic world, in stochastic case, we got additional dt - factor. 

So now we can rewrite Y as process depending on simple brownian motion:

Now applying Ito integration formula we got solution for Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator. :

Finally recalling thatUnknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator. 

We get the solution: Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.