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The integrating factor for the differential equation dP/dt + k2 P = k1 e^(-k1 t) is

1. e^(-k1 t)
2. e^(-k2 t)
3. e^(k1 t)
4. e^(k2 t)

Correct answer: e^(k2 t)

Solution

The integrating factor is derived from the coefficient of P in the differential equation, which is k2. The integrating factor is e raised to the integral of k2 with respect to t, resulting in e^(k2 t), allowing us to simplify the equation for easier integration.

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