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Math Help - coupled equations

  1. #1
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    coupled equations



    dx/dt - 5x = -3Ae^2t

    ---->

    2x-5x^2 = -3Ae^2t

    what should i do to get the answer?

    thx
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Hikari Clover View Post


    dx/dt - 5x = -3Ae^2t

    ---->

    2x-5x^2 = -3Ae^2t

    what should i do to get the answer?

    thx

    First this is a linear constant coefficeient non-homogeneous ODE. So the general solution is the sum of the general solution of the homogeneous problem:

    \frac{dx}{dt} - 5x = 0\ \ \ \ \ (1)

    and a particular integral of:

     <br />
\frac{dx}{dt} - 5x = -3Ae^{2t}\ \ \ \ \ (2)<br />

    You should know how to find the general solution to (1) , and to find a particular integral of (2) try a solution of the form:

     <br />
x(t)=k e^{2t}<br />

    CB
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