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Math Help - find x(t) : ( a - x(t) )^2 = c*x'(t)

  1. #1
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    find x(t) : ( a - x(t) )^2 = c*x'(t)

    hello everyone, im trying to do a voltage analysis for some electric circuit in my homework assingment and deduced the following equation:

    (a - v(t) )^2 = c*v'(t)

    a,c - constants
    now i dont remember much from the differential equations course i took in first year, but i dont think we learned how to solve a none linear equation

    so can anyone explain to me how to solve such a thing ?

    thanks
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  2. #2
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    It's separable...

    So \displaystyle (a - v)^2 = c\,\frac{dv}{dt}

    \displaystyle \frac{1}{c} = (a - v)^{-2}\,\frac{dv}{dt}

    \displaystyle \int{\frac{1}{c}\,dt} = \int{(a - v)^{-2}\,\frac{dv}{dt}\,dt}

    \displaystyle \int{\frac{1}{c}\,dt} = \int{(a - v)^{-2}\,dv}.

    You should be able to solve now.
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  3. #3
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    oh right !!, thats how u do that

    thanks man
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