Differential Eq...

$$\dfrac{dy}{dx}=\dfrac{4x+2y+1}{x-2y+3}$$ is a differential equation of the type:

The solution of $$\dfrac{dy}{dx}=\dfrac{1+y^{2}}{\sec x}$$ is

The solution of $$\dfrac{dy}{dx}+2x=e^{3x}$$ is:

The solution of $$x^{3}dy-y^{3}dx=0$$ is:

The solution of $$\displaystyle \frac{dy}{dx}=\displaystyle \frac{3(y+1)}{x-2}$$ is:

The solution of $$\dfrac{d^{2}y}{dx^{2}}=xe^{x}+1$$ is:

The solution of the differential equation
$$\displaystyle \frac{dy}{dx}=\displaystyle \frac{xy+y}{xy+x}$$ is

The solution of $$\dfrac{dy}{dx}=\text{cosech }y$$ is:

The solution of $$(1+e^{x})ydy=e^{x}dx$$ is:

The solution of the differential equation $$(1+x^{2})\displaystyle \frac{dy}{dx}=2 x \cot y$$, is: