Let `y=f(x)` is solution of differential equation `cos^(2)xdy-cos^(4)xdx=(tan2x)ydx,|x|le(pi)/(4)` and `f((-pi)/(6))=(-3sqrt(3))/(8),` then

Solution of the equation cos^(2)x(dy)/(dx)-(tan2x)y=cos^(4)x,|x|<(pi)/(4), wheny ((pi)/(6))=(3sqrt(3))/(8)is

STATEMENT-1 : The solution of differential equation cos^(2)x.(dy)/(dx) - y tan 2x = cos^(4)x , where |x| lt (x)/(4) and y((pi)/(6)) = (3sqrt(3))/(8) is y = (sin 2x)/(2(1-tan^(2) x) and STATEMENT-2 : The integrating factor of the given differential equation is |(1- tan^(2)x)| .

The solution of differential equation 4xdy - ydx = x^(2) dy is

Solution of differential equation x(xdx-ydy)=4sqrt(x^(2)-y^(2))(xdy-ydx) is

Let y(x) be the solution of the differential equation (dy)/(dx)+(3y)/(cos^(2)x)=(1)/(cos^(2)x) and y((pi)/(4))=(4)/(3) then vaue of y(-(pi)/(4)) is equal to (a)-(4)/(3)(b)(1)/(3)( c) e^(6)+(1)/(3)(d)3

The solution of the differential equation xdx+ydy+(xdy-ydx)/(x^(2)+y^(2))=0 , is