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Which of the following is a solution to the differential equation dx(t)/dt + 3x(t) = 0 ?

1. x(t) = 3e^(−t)
2. x(t) = 2e^(−3t)
3. x(t) = −(3/2)t²
4. x(t) = 3t²

Correct answer: x(t) = 2e^(−3t)

Solution

The correct option, x(t) = 2e^(−3t), satisfies the differential equation because it represents an exponential decay with a rate of 3, which matches the coefficient of x(t) in the equation. This solution can be verified by substituting it back into the equation and confirming that both sides are equal.

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