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    I am really struggling with this differential problem please can someone help:

    The equation of a motion of a train is given by: m.dv/dt = mk(1-e^-t)-mcv , where v is the speed, t is the time and m, k and c are constants. Determine a general equation for the speed, v given that v=0 and t=0.

    I understand i should use the integration factor but am just getting stuck any help would be appreciated.
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    You can start by cancelling the ms. Then you need to write it in the form
    \dfrac{dv}{dt} = p(t)v + q(t)

    That is, identify what your p(t) and q(t) are, and then just follow the usual method.
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    i woudl normally keep it in the format dv/dt + f(t) V = g(t)

    then just a case of finding the IF, mulitplying by this then d/dt [ f(t). v ] = g(t)

    then just integrate?
 
 
 
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