General solution of differential equation: $\large\frac{dy}{dx}$$+x \sin 2y=x^3 \cos ^2 y$

Question

$(a)\; \tan y=\frac{1}{2}(x^2-1)e^{x^2}+c \\ (b)\;\tan y=\frac{1}{2}(x^2+1)e^{x^2}+ce^{x^2} \\ (c)\;\tan x=\frac{1}{2}(x^2+1)e^{y^2}+ce^{x^2} \\ (d)\;\tan x=\frac{1}{2}(x^2-1)+ce^{-x^2} $