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

The solution for sin^2(y)dx+xsin(2y)dy=0 is

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sin^2(y)dx+xsin(2y)dy=0

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

y = arcsin (\frac{c _{1}}{x}) + 2 πn, y = π + arcsin (- \frac{c _{1}}{x}) + 2 πn, y = arcsin (- \frac{c _{1}}{x}) + 2 πn, y = π + arcsin (\frac{c _{1}}{x}) + 2 πn

Solution steps

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

Solve separable ODE:

y = arcsin (\frac{c _{1}}{x}) + 2 πn, y = π + arcsin (- \frac{c _{1}}{x}) + 2 πn, y = arcsin (- \frac{c _{1}}{x}) + 2 πn, y = π + arcsin (\frac{c _{1}}{x}) + 2 πn

y = arcsin (\frac{c _{1}}{x}) + 2 πn, y = π + arcsin (- \frac{c _{1}}{x}) + 2 πn, y = arcsin (- \frac{c _{1}}{x}) + 2 πn, y = π + arcsin (\frac{c _{1}}{x}) + 2 πn

\int sin^{3} (7 x) d x

\int 8 e^{4 x} d x

y = 6 x

\int_{- 1}^{1} \frac{2}{x ^{2} + 1} d x

\frac{d ^{2}}{d x ^{2}} ((x^{3} + 8 x)^{12})

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