The general solution of the differential equation $\frac{dy}{dx} + y\cot x = 2\cos x$ is (Where C is an arbitrary constant)

For $|x| < 1$, if $x = \cos\left(\frac{1}{a}\log y\right)$, then

The solution of the differential equation $9+y^2\dfrac{dy}{dx}=x^2$ is :

[Where $C$ is an arbitrary constant]

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x^2+xy+y^2}{x^2}$ for $x>0, y>0$ at $x=1, y=2$ is

The differential equation representing family of circles with centre at origin and radius r units is-

The solution of the differential equation $x\frac{dy}{dx} = 2x^2 + 1$; $x \neq 0$ with $y = 1$ when $x = 1$, is

Given differential equation, (1 + y²)dx = (tan⁻¹y - x)dy, then which of the following is/are true?

(A) Integrating factor = tan⁻¹x

(B) Integrating factor = tan⁻¹y

(C) Integrating factor = $e^{tan⁻¹y}$

(D) Degree = 1

Choose the correct answer from the options given below: