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Math Help - Differential equations

  1. #1
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    Differential equations

    I'm struggling with an assignment question.

    Solve each of the following differential equations to find the corresponding growth function. (show all necessary calculus)

    i. dQ/dt=kt where k>0 t>= 0 Q(0)= Qo

    ii. dy/dt=a(q-y) where t>=0 y(0)=0, a and q are constants with a>0, q>0
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  2. #2
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    Quote Originally Posted by phillipvdw2001 View Post
    I'm struggling with an assignment question.

    Solve each of the following differential equations to find the corresponding growth function. (show all necessary calculus)

    i. dQ/dt=kt where k>0 t>= 0 Q(0)= Qo
    \frac{dQ}{dt}= k~t

    This is of variables seperable type so:

    <br />
\int dQ = \int k~ t~ dt + C<br />

    where C is determined from your initial conditions

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by phillipvdw2001 View Post
    ii. dy/dt=a(q-y) where t>=0 y(0)=0, a and q are constants with a>0, q>0
    Again variables seperable:

    \frac{dy}{dt}=a(q-y)

    so:

    \frac{1}{a(q-y)}~\frac{dy}{dt}=1

    and so:

    <br />
\int \frac{1}{a(q-y)}~dy = \int dt +C<br />

    Again determine C from the initial conditions

    RonL
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  4. #4
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    For solution see the attachment
    Attached Files Attached Files
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