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Solve the differential equation?

Solve the differential equation e^x dx+(e^x cot(y)+2y csc(y))dy=0.

M=e^x

N=e^x cot(y)+2y csc(y)

My=0

Nx=e^x cot(y)

Obviously isn't exact.

What to do next?

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1 Answer

Multiply your equation by siny. You will obtain:

            ex sinydx + excosy dy + d(y 2) = 0

or   

                              d(ex siny) + d(y2) = 0   

Thus, your solution is 

                                   ex siny + y2 = const     (y is not equal to zero)