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

The solution of $${x^3}{{dy} \over {dx}} + 4{x^2}\tan y = {e^x}\sec y$$ satisfying y (1) = 0, is

The solution of the equation $${{dy} \over {dx}} + {1 \over x}\tan y = {1 \over {{x^2}}}\tan y\sin y$$ is

The solution of differential equation $$(x{y^5} + 2y)dx - xdy = 0$$, is

A curve passes through (2, 0) and the slope of the tangent at P(x, y) is equal to $${{{{(x + 1)}^2} + y - 3} \over {x + 1}}$$ then the equation of the curve is