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Please help in solving this differential equation?
sin y (dy/dx) = cos y (1 - x cos y)
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- ecapS trebliHLv 610 years agoFavorite Answer
Let u = cos(y)
du/dx = - sin(y) dy/dx = x u^2 - u
==> du/dx + u = x u^2
u'/u^2 + 1/u = x ; thus the variables are separated
To simplify, let w = 1/u
Then - w' + w = x or w' - w = - x
This is a linear 1st order differential equation; solve for w in the standard way.
Once you have done this, use the formula y = cos^(-1) (1/w)
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