TIFR ECE 2021 | Question: 4

Question

The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider the following statements?

1. System is memoryless.
2. System is causal.
3. System is stable.

Which of the following fact about the statements above is true? (Hint: You may try answering by finding the impulse response)

• A. Only $(1)$ is correct.
• B. Only $(1)$ and $(2)$ are correct.
• C. All $(1), (2)$ and $(3)$ are correct.
• D. Only $(2)$ and $(3)$ are correct.
• E. None of the above