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About Dr. Nyayapati Swami
Expertise
I can help you in solving first and second order differential equations. Questions must be at the Undergraduate level. Do not expect me to do all your homework.. If you have a homework question with no clues on how to go about, I will only give you some pointers on solving them.

Experience
Ph.D. in Mathematics with more than 15 years of teaching.
In addition to undergraduate calculus, I taught many more advanced subjects like Complex Analysis, General Topology, Numerical Analysis, Operations Research, Graph Theory, Mathematical Analysis, Mathematical Economics, Optimisation Theory.

Education/Credentials
Ph.D. (University of Toledo, USA)

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Differential Equations - differential equations

Expert: Dr. Nyayapati Swami - 9/29/2009

Question
The general solution of the differential equation sin y dy = cos y (1 - x cos y) dx

Answer
Let v = cosy
Then
dv/dx = - siny dy/dx
     = - cosy (1 - xcosy)
     = - v(1-xv)
Now let
u = 1/v (or you could have chosen u = secy in the beginning)

Then
du/dx = - (1/v^2) dv/dx
     = (1/v^2) v (1-xv)
     = (1/v) ( 1- xv)
     = 1/v - x
     = u - x
This gives you a linear equation
du/dx - u = -x

Solve this to find u, and then revert back to y.

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