If the slope of the tangent to the curve $y = y(x)$ at any point $(x, y)$ is $\frac{2x}{y^2}$ and the curve passes through the point $\left(\frac{1}{\sqrt3}, 1\right)$, then equation of curve is

The sum of order and degree of the differential equation $(x^2\frac{d^2y}{dx^2})^{3/4} = 5(\frac{dy}{dx})^2 - 3$ is equal to

General solution of the differential equation $x(xdy - ydx) = y\,dx$ is :(where c is an arbitrary constant)

If the order and degree of the differential equation $y + \dfrac{dy}{dx} = \int y\,dx$ are m and n respectively, then (m - n) is equal to

Match List-I with List-II

Choose the correct answer from the options given below:

Which of the following statements is/are true?

(A) $(\tan^{-1} y - x)dy = (1 + y^2)dx$ is a differential equation where variables are separable.

(B) $(1 + x^2)dy + 2xydy = \cot x \ dx (x \neq 0)$ is a first order linear differential equation.

(C) $(4x + 6y + 5)dy - (3y + 2x + 4)dx = 0$ is not a homogeneous differential equation.

(D) $(xy)dx - (x + y^2)dy = 0$ is a homogeneous differential equation.

Choose the correct answer from the options given below:

General solution of the differential equation $\frac{dy}{dx} = e^{\frac{x^2}{2}} + xy$ is