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    I need to find the general solution of the differential equation:

     \frac{dy}{dx} = 3x^{2}(y-1)

    Im confused what it means by general solutions, do i need to integrate it?
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    Separate the variables, integrate then and put it in the form you desire
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    Yup, integrate and you'll have a constant - that's your general solution. 2nd order DEs will have 2 constants, 3rd will have 3 etc.
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    By separating the variables, do you mean:

     \int \frac{1}{y-1} dy = \int 3x^2 dx
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    (Original post by bikinmad)
    By separating the variables, do you mean:

     \int \frac{1}{y-1} dy = \int 3x^2 dx
    That's correct.
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    I found the general solution to be:

     y = Ae^{x}^{3} +1

    It says in the question, 'Check if the general solution contains all the solutions of this equation?' I dont really understand what it means by this?
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    Let y2 be another solution to the differential equation, so  \frac{dy_2}{dx} = 3x^{2}(y_2-1)

    Then let z=y-y_2, can you do anything with \frac{dz}{dx}?
 
 
 
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