Calculus AB

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Verify if the given equations are solutions to the differential equation.

dy/dt=k(y-a)

i) y=1-ae^(kt)
ii) y=a+Ce^(kt)

  • Calculus AB -

    dy/dt=k(y-a) ... (1)

    i) y=1-ae^(kt) (particular solution)
    differentiate y w.r.t. t:
    d(1-ae^(kt))/dt
    = k(e^(kt)+a)-ka
    = ky-ka
    = k(y-a)
    = right-hand side, QED

    ii) y=a+Ce^(kt)
    differentiate with respect to t:
    dy/dt
    =Cke^(kt)
    =k(a+Ce^(kt))-ka
    =ky-ka
    =k(y-a)
    =right-hand side QED

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