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find the general solution of the following first order differential equation.

u(t): du/dt = u /t+2t

pls show all working

  • differential equations -

    I assume you mean
    du/dt = (u/t) + 2t and not
    u/(t + 2t) = u/(3t)

    Your D.E. is of the form
    du/dt + Pu = Q
    where P = -1/t and Q = 2t

    The method of "integrating factors" can be used. Your textbook should have an explanation of the method.

    There is a function rho(t) given by
    rho(t) = exp(integral of P(t)dt)

    such that the solution is
    rho(t)*u
    = integral of (rho*Q) + C

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