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Math Help - General solution

  1. #1
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    General solution

    find general solution of

    xy(1+x^2)dy/dx-(1+y^2)=0

    Solution:

    this becomes

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

    getting x's on one side and y's on the other
    then the difficulties start, i tried to get the dy on the side of the y's to differenciate but when i do this i get 1/dy which seems weird

    then tried

    x(1+x^2) dy = (1/y+y) dx and differenciated left side(x's) with respect to y and the right side (y's) with respect to x which seems weird...
    is this right?
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by fitzgilbert View Post
    find general solution of

    xy(1+x^2)dy/dx-(1+y^2)=0

    Solution:

    this becomes

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

    ...
    This is only a try because I don't know what you are supposed to do:

    \frac{x(1+x^2)}{dx}=\frac{1+y^2}{y \cdot dy}~\implies~ \frac1{x(1+x^2)} \cdot dx=\frac{y}{1+y^2} \cdot dy
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  3. #3
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by earboth View Post
    This is only a try because I don't know what you are supposed to do:

    \frac{x(1+x^2)}{dx}=\frac{1+y^2}{y \cdot dy}~\implies~ \frac1{x(1+x^2)} \cdot dx=\frac{y}{1+y^2} \cdot dy
    Integrate both sides and then solve for y.
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