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differentiate both side with respect to x : (dy/dx)e^(-2x)+y(-2e^(-2x)) = 2+2y(dy/dx)
rearrange it : (-2y+e^(-2x))(dy/dy) = 2 + 2ye^(-2x) ==> dy/dx = ( 2 + 2ye^(-2x) ) / ( -2y+e^(-2x) )

The first thing to do is to establish the purpose of the essay – in doing this, we want to break down the question that is being answered and examine the components of it. This sounds like it is just an e...

Disguise is the key theme in Twelfth Night and this question therefore opens up a discussion with a lot of scope. Details about characters can be mentioned and it can also be linked to other themes. Start...

Originally the number of rabbits was 200. We therefore need to find 25% of 200 and then increase the value of 200 by the 25%, we will then know how many rabbits there are after the 25% increase. 25/100 x ...

Let f denote an integral sign, I will write the integrand in square brackets. We can use integration by parts to integrate ln(x), the "trick" here is to imagin ln(x) as 1 x ln(x). Integ...