SOLUTION: Solve the differential equation: y’ = csc x - y cot x *
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Question 1167385: Solve the differential equation: y’ = csc x - y cot x *
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ -\ y\,\cot(x))
}{dx}\ +\ y\,\cot(x)\ =\ \csc(x))
Let dx}\ =\ \sin(x))
and multiply through
\frac{dy(x)}{dx}\ +\ \cos(x)y(x)\ =\ 1)
Substitute }{dx}\ =\ \cos(x))
\frac{dy(x)}{dx}\ +\ \frac{d\sin(x)}{dx}y(x)\ =\ 1)
Reverse Product Rule
y(x)\]\ =\ 1)
Integrate wrt 
y(x)\]\,dx\ =\ \int\,1\,dx )
y(x)\ =\ x\ +\ C)
\ =\ \csc(x)(x\ +\ C))
John
My calculator said it, I believe it, that settles it
I > Ø
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