The general solution of the differential equation $\dfrac{dy}{dx} = 1+x+y+xy$ is: (where $C$ is an arbitrary constant)

(A) $1+y = x+\dfrac{x^2}{2}+C$

(B) $\log_e|1+y|^2 = x^2+2x+C$

(C) $\log_e|1-y| = x-\dfrac{x^2}{2}+C$

(D) $\log_e|1+y| = x+\dfrac{x^2}{2}+C$

Choose the correct answer from the options given below:

The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$, where m is arbitrary constant, is

Which of the following differential equations has $y=x$ as one of the particular solution?

Match List-I with List-II

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The differential equation representing family of curves $y = ae^{mx} + be^{nx}$, where $a$ and $b$ are arbitrary constants, is

Solution of differential equation $x dy - y dx = 0$ respresents :

The solution of the differential equation $\frac{dy}{dx} = \frac{x+y}{x-y}$ is