Match List-I with List-II | List-I | List-II | |---|---| | (A) Integrating factor of $xdy - (y + x^2)dx = 0$ | (I) $x^2$ | | (B) Integrating factor of $xdy + (2y + x^2)dx = 0$ | (II) $x^3$ | | (C) Integrating factor of $(3y - x^2)dx + xdy = 0$ | (III) $x$ | | (D) Integrating factor of $(y + 3x^2)dx + xdy = 0$ | (IV) $\frac{1}{x}$ | Choose the correct answer from the options given below:

The solution of the differential equation $\frac{dy}{dx} = x^2 + x + \frac{1}{x}$ is

Let $y(x) = a(x + 1) \log(x + 1) + bx + 5$ be the solution of the differential equation e$^\frac{dy}{dx} = x + 1_{;}y(0) = 5$, then the value of $(a + b)$ is:

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

For the differential equation $\frac{d}{dx}\left(\frac{d^3y}{dx^3}\right)+\left(\frac{dy}{dx}\right)^3+y+x=7$, which of the following statements are True?

A. Order of differential equation is 4

B. Number of arbitrary constants in the particular solution of differential equation are 4

C. Number of arbitrary constants in the general solution of the differential equation are 4

D. Degree of differential equation is 3

Choose the correct answer from the options given below:

The general solution of the differential equation $(y-x)dy + (x+y)dx = 0$ is: (where C is arbitrary constant)

If $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$, then the order and degree of the differential equation are