- #1
L.D.50
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Homework Statement
dx/dy = cos(y) - xtan(y)
I need to find the general solution of the problem
Homework Equations
y' + Py = Q
Where P and Q are functions of x
dy/y = - Pdx
ln(y) = -integral(Pdx)+c
y = e^(-int(Pdx)+c)
The Attempt at a Solution
Now I have no idea what to do to be honest. Nothing I try and do to separate the variables to get it in the form y' + Py = Q works. There is always something left over that complicates things even more. I've tried many trig substitutions, to no avail. Here is one thing I tried.
dx/x = [(1/x)cosy - tany]dy
dx/x = (1/x)cosy dy - tan y dy
But then I have two dy terms. Is this correct? I really have no idea how to proceed from here.
Ive also tried:
dx/dy = cos(y) - xtan(y)
(dx/dy)cosy = cos^2(y) - xsiny
(dx/dy)2cosy = 1 + cos(2y) - 2xsiny
But now once again I have no idea how to proceed. Any help would be greatly appreciated!