The differential equation $\frac{dy}{dx} = \frac{1}{ax + by + c}$,where $a, b, c$ are all non-zero real numbers,is

Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function. If $6 \int_{1}^{x} f(t) dt = 3xf(x) + x^{3} - 4$ for all $x \ge 1$, then the value of $f(2) - f(3)$ is

General solution of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ is

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:

Let $y(x)$ be a solution of the differential equation $(1+e^x) y^{\prime}+y e^x=1$. If $y(0)=2$,then which of the following statements is (are) true?
$(A)$ $y(-4)=0$
$(B)$ $y(-2)=0$
$(C)$ $y(x)$ has a critical point in the interval $(-1,0)$
$(D)$ $y(x)$ has no critical point in the interval $(-1,0)$

The solution of the differential equation,$(x + 2y^3) \frac{dy}{dx} = y$ is :