The general solution of the differential equation $$x^2 d y-2 x y d x=x^4 \cos x d x$$ is

The curve passing through the point $$(1,2)$$ given that the slope of the tangent at any point $$(x, y)$$ is $$\frac{3 x}{y}$$ represents

The integrating factor of the differential equation $$\left(2 x+3 y^2\right) d y=y d x(y>0)$$ is

The equation of the curve passing through the point $$(1,1)$$ such that the slope of the tangent at any point $$(x, y)$$ is equal to the product of its co-ordinates is