cos^(2)x(dy)/(dx)+y=tan x

Find the general solution of the differential equations: quad cos^(2)x(dx)/(dy)+y=tan x(0<=x<(pi)/(2))

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)| .

An integrating factor of the differential equation cos^(2) x (dy)/(dx) - (tan 2x) y = cos^(4) x is

Solve the following differential equations.(2) cos^2x dy/dx+y=tan x

If y=tan x. cos^(2)x then (dy)/(dx) will be-

If y=x+tan x , show that cos^(2) x. (dy)/(dx)=2-sin^(2)x .

(dy)/(dx)=tan^(2)(x+y)

The integrating factor for (dy)/(dx) - 2y tan x = cos x is :

Solve the differential equation: (i) (1+y^(2))+(x-e^( tan ^(-1)y))(dy)/(dx)=0 (ii) x(dy)/(dx)+cos^(2)y=tan y(dy)/(dx)