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I want to verify that the form of a particular solution satisfies the following ODE:

v' + (b/m)v = u/m

with

v_{part}= ∫e^{-(b/m)(t-r)}(u(r)/m) dr

where the limits are from 0 to t

So I tried to differentiate v with respect to t, in order to substitute it back into the equation. But, how do you do that when the integral is with respect to r? Is there a need to change variables? How can you do this?

Cheers

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# Derivative of a Convolution

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