The general solution of the differential equation $\dfrac{dy}{dx}=2^{-y}$ is:

(where $c$ is an arbitrary constant)

The solution of the differential equation $\frac{dy}{dx} = \frac{6}{x^2}$; $y(1) = 3$ is :

Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :

Match List-I with List-II

Choose the correct answer from the options given below:

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

Which of the following are linear first order differential equations?

(A) $\frac{dy}{dx} + P(x)y = Q(x)$

(B) $\frac{dx}{dy} + P(y)x = Q(y)$

(C) $(x - y)\frac{dy}{dx} = x + 2y$

(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$

Choose the correct answer from the options given below:

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