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?
- System is memoryless.
- System is causal.
- System is stable.
Which of the following fact about the statements above is true? (Hint: You may try answering by finding the impulse response)
- Only $(1)$ is correct.
- Only $(1)$ and $(2)$ are correct.
- All $(1), (2)$ and $(3)$ are correct.
- Only $(2)$ and $(3)$ are correct.
- None of the above