The particular solution of the differential equation $\frac{dy}{dx} = 8yx$ when $y = 1$ at $x = 0$

Consider the differential equation $\frac{dy}{dx} + y \tan x = \sec x$, then which of the following statements are correct?

(A) It is homogeneous

(B) It has $\sec x$ as its integrating factor

(C) It's general solution is $y \sec x = \tan x + c$, where c is arbitary constant.

(D) It's degree is not defined

Choose the correct answer from the options given below:

The differential equation $y = xp + \sqrt{x^2 p^3 + 4}$ where $p = \frac{dy}{dx}$ is :

(A) of order 1

(B) of degree 1

(C) of order 2

(D) of degree 3

Choose the correct answer from the options given below :

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(C) second order and second degree

(D) second order

Choose the correct answer from the options given below :

Solution of differential equation $\frac{dy}{dx} = e^{x+y} - xe^y$ is

If curve represented by differential equation $x \frac{dy}{dx} + y = e^x$ passes through (1, 1), then $y(-1)$ is :

The general solution of the given differential equation $dy + (2y - e^{-2x})dx = 0$, is:

[where c is an arbitrary constant]