The solution of $(y-3 x^2) d x+x d y=0$ is

The general solution of the differential equation,$\sin 2x \left( \frac{dy}{dx} - \sqrt{\tan x} \right) - y = 0$ is

If $x dy + (y + y^2 x) dx = 0$ and $y = 1$ at $x = 1$,then

Let $f$ be a real-valued differentiable function on $\mathbb{R}$ (the set of all real numbers) such that $f(1)=1$. If the $y$-intercept of the tangent at any point $P(x, y)$ on the curve $y=f(x)$ is equal to the cube of the abscissa of $P$,then the value of $f(-3)$ is equal to

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^{x} f(t) dt = 5x f(x) - x^5 - 9$ for all $x \geq 1$,then the value of $f(3)$ is:

The solution of the differential equation $\frac{dy}{dx} - y \tan x = e^x \sec x$ is