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Math Help - Ordinary Differential Equation

  1. #1
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    Ordinary Differential Equation

    I've been looking at this for a while, I don't really know where to start. The question is: what is the general solution to the following ordinary differential equation:

    dy/dx = √(4x+2y-1)

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by Unoticed View Post
    I've been looking at this for a while, I don't really know where to start. The question is: what is the general solution to the following ordinary differential equation:

    dy/dx = √(4x+2y-1)

    Any help would be appreciated.
    y ' = \sqrt{4x+2y-1}
    Let z=4x+2y-1 then z'=4+2y'\implies y' = \frac{1}{2}z' -2.
    Substitute to get,
    \frac{1}{2}z' - 2 = \sqrt{z}
    That is Bernoulli Equation.
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  3. #3
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    Thanks a lot mate
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  4. #4
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    Hey, I've looked at some stuff on the Bernoulli Equation and I don't understand how to get from that to a general solution. Do I have to make another substitution?
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  5. #5
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    Actually, the equation is separable.
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  6. #6
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    really? how so? thats the first thing I tried but I couldnt get it
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