What is the solution for 8cos^2(y)dx+csc^2(x)dy=0,y(pi/(12))= pi/4 ?

The solution for 8cos^2(y)dx+csc^2(x)dy=0,y(pi/(12))= pi/4 is y=arctan(-4(x-1/2 sin(2x))+c_{1})+pin

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8cos^2(y)dx+csc^2(x)dy=0,y(pi/(12))= pi/4

8 cos^{2} (y) d x + csc^{2} (x) d y = 0, y (\frac{π}{12}) = \frac{π}{4}

y = arctan (- 4 (x - \frac{1}{2} sin (2 x)) + c_{1}) + πn

Solution steps

8 cos^{2} (y) d x + csc^{2} (x) d y = 0

Solve separable ODE:

y = arctan (- 4 (x - \frac{1}{2} sin (2 x)) + c_{1}) + πn

y = arctan (- 4 (x - \frac{1}{2} sin (2 x)) + c_{1}) + πn

\frac{d}{d x} (\frac{a + b x + c x ^{2}}{x})

\frac{d y}{d x} + 4 y = e^{- 4 x}

\frac{\partial}{\partial x} (3 x^{2} - 3)

\int \frac{x - 1}{x ^{2} ( x + 1 ) ^{2}} d x

t an g e n t f (x) = \frac{7}{x ^{2}} - 6 x^{2}, at x = 5

What is the solution for 8cos^2(y)dx+csc^2(x)dy=0,y(pi/(12))= pi/4 ?
The solution for 8cos^2(y)dx+csc^2(x)dy=0,y(pi/(12))= pi/4 is y=arctan(-4(x-1/2 sin(2x))+c_{1})+pin