What is the solution for cos^2(y)sin(x)dx+sin(x)cos(x)dy=0 ?

The solution for cos^2(y)sin(x)dx+sin(x)cos(x)dy=0 is y=arctan(-ln(tan(x)+sec(x))+c_{1})+pin

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cos^2(y)sin(x)dx+sin(x)cos(x)dy=0

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

y = arctan (- ln (tan (x) + sec (x)) + c_{1}) + πn

Solution steps

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

Solve separable ODE:

y = arctan (- ln (tan (x) + sec (x)) + c_{1}) + πn

y = arctan (- ln (tan (x) + sec (x)) + c_{1}) + πn

\frac{d y}{d x} = 2 x^{4} y, y > 0

\frac{d y}{d x} = 2 x (y^{2} + 1)

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

(x + 1) d x + e^{y} d y = 0

y^{^{'}} = y - \frac{y ^{2}}{3}

What is the solution for cos^2(y)sin(x)dx+sin(x)cos(x)dy=0 ?
The solution for cos^2(y)sin(x)dx+sin(x)cos(x)dy=0 is y=arctan(-ln(tan(x)+sec(x))+c_{1})+pin