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Math Help - Differential Equations Help pls

  1. #1
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    Differential Equations Help pls

    1.Using separation of variable , solve the differential Equation

    dy/dx = ((3x^2+4x+2)/(2(y-1)))

    y(0) = -1

    Thank you
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  2. #2
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    Re: Differential Equations Help pls

    $\dfrac{dy}{dx}=\dfrac{3x^2+4x+2}{2(y-1)}$

    $2(y-1)dy=(3x^2+4x+2)dx$

    you should be able to finish it from here.
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  3. #3
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    Re: Differential Equations Help pls

    So y^2 -2y = x^3+2x^2+2x+C

    what should i do with y^2-2y(2 y variable) that is the question ?

    I'm newbie with dif equ i don't have any experience with problem
    i just learn a easy seperation problem
    ex dy/dx = y that y has only one variable on the left side
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  4. #4
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    Re: Differential Equations Help pls

    Your implicit solution is fine, but if you really want to get y explicitly in terms of x, complete the square.
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  5. #5
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    Re: Differential Equations Help pls

    Complete the square is the basic but I'm still don't know
    How to complete the square in this case

    Anybody solution pls??
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  6. #6
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    Re: Differential Equations Help pls

    Come on...

    $\displaystyle \begin{align*} y^2 - 2y &= y^2 - 2y + \left( -\frac{2}{2} \right)^2 - \left( -\frac{2}{2} \right) ^2 \\ &= y^2 - 2y + (-1)^2 - (-1)^2 \end{align*}$

    Finish it.
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