The governing differential equations connecting the output

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The governing differential equations connecting the output y(t) and the input x (t) of four continuous time systems are given in the List-I and List-II respectively. Match List-I (Equation) with List-II (System Category) and select the correct answer using the code given below the Lists—

1. A B C D
  3 2 1 4
2. A B C D
  4 1 5 3
3. A B C D
  3 1 5 4
4. A B C D
  4 2 1 3

Correct Option: C

(A) 2t	dy	+ 4y = 2tx
	dt

● Since, there is no constant hence linear.
● t factor means time-variant.
● dy/dt term means dynamic which gives A → 3

(B) y	dy	+ 4y = 2x
	dt

● Since, there is no constant term mean linear
● No time varying term means time-invariant.
● dy/dt term means dynamic which gives B → 1
Since, these options given only in code (C). So, no need to solve further.
Hence, alternative (C) is the correct choice.