Question

Assume a is a non-zero constant, and use C for any constant of integration that you may have in your answer. dp/dt=2p+a solve differential equation p=

Answer 1

Answer:

$p=\dfrac{1}{2}(e^{2t + C'}-a)$

Step-by-step explanation:

We are given the following differential equation:

$\displaystyle\frac{dp}{dt} = 2p + a$

where a is a non zero constant.

Solving the differential equation:

$\displaystyle\frac{dp}{dt} = 2p + a\\\\\frac{dp}{2p+a} = dt\\\\\text{Integrating both sides}\\\\\int \frac{dp}{2p + a} = \int dt\\\\\frac{1}{2}\ln(2p+a) = t + C\\\\\text{where C is the constant of integration.}\\\\\ln(2p+a) = 2(t+C)\\\\2p+a = e^{2t + C'}\\2p = e^{2t + C'}-a\\\\p=\dfrac{1}{2}(e^{2t + C'}-a)$