The solution of the differential equation

$ (x+1) \frac{d y}{d x}-y=e^{3 x}(x+1)^{2} $ is

If $$\left(1+x^2\right) d y+2 x y d x=\cot x d x$$, then the general solution be

$$\left( {{{dy} \over {dx}}} \right)\tan x = y{\sec ^2}x + \sin x$$, find general solution

Solution of $$\left( {{{x + y - 1} \over {x + y - 2}}} \right){{dy} \over {dx}} = \left( {{{x + y + 1} \over {x + y + 2}}} \right)$$, given that y = 1 when x = 1 is