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Math Help - Differential equations - seperation of variables

  1. #1
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    Differential equations - seperation of variables

    Solve the given differential equation by Separation of variables.

    (1+x^4)dy + x(1+4y^2)dx = 0, y(1)=0
    (3x^2 + 9xy + 5y^2)dx (6x^2 +4xy)dy = 0, y(2) = -6
    (3y^2-x^2 / y^5)dy/dx + x/2y^4 = 0, y(1) = 1
    Dr/dQ + rsecQ = cosQ
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  2. #2
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    Quote Originally Posted by wyasser View Post
    Solve the given differential equation by Separation of variables.

    (1+x^4)dy + x(1+4y^2)dx = 0, y(1)=0
    (3x^2 + 9xy + 5y^2)dx (6x^2 +4xy)dy = 0, y(2) = -6
    (3y^2-x^2 / y^5)dy/dx + x/2y^4 = 0, y(1) = 1
    Dr/dQ + rsecQ = cosQ
    It will help people to answer your question if you write out your equations using LATEX.

    For the first one:

    (1+x^4)dy + x(1+4y^2)dx = 0

    Here divide both sides by (1+x^4)(1+4y^2), this will leave you with:

    \int\frac{x}{1+x^4}dx + \int\frac{1}{1+4y^2}dy = 0

    Hint, for the x variable consider using partial fractions to simplify the equation before you try and integrate.

    The second one is a little harder.

    (3x^2 + 9xy + 5y^2)dx - (6x^2 +4xy)dy = 0

    For this one I would suggest using a substitution to simplify the equation a little before you attempt to separate the variables.

    Let y = vx where v = v(x), if we differentiate this equation with respect to x we get

    dy = xdv + vdx.

    Substitute in these 2 values and see how you go.

    When you've done these try and see what you can manage with the last two.

    Hope this helps
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