What is the population size at the time ‘t’?

$$\int \frac{dx}{\sin^{2}x \cdot \cos^{2}x}$$ equals:

If $$\log(x + y) - 2xy = 0$$​, and $$y(0) = 1,$$​ then $$y'(0)$$  is:

An integrating factor of the differential equation $$(2x^2+y^2+x)dx+xy dy=0$$ is​

Tangent at which point of the curve $$x=ct^3, y=\frac{c}{t^3}$$ is parallel to the line $$y=2x-1?$$​​

If $$\frac {dp}{dt}=\frac{1}{2p}$$ and $$p=1$$ when $$t=0$$, then $$p=3$$, when t is​

A particular solution of the differential equation $$x^2 \frac{d^2y}{dx^2} - 2x(1 + x) \frac{dy}{dx} + 2(1 + x)y = x^3$$ is​

The differential equation of all circles touching x-axis at origin is