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Math Help - Non-Linear and non separable differential equation

  1. #1
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    Non-Linear and non separable differential equation

    How can i solve this equation as it is non-linear and non seperable, i cant use the integrating factor as Q(x) does not exist and i cant seperate so that x and y are separate.

    x.(dy/dx)=-3y + 6x

    some tips please
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by metalkakkarot View Post
    How can i solve this equation as it is non-linear and non seperable, i cant use the integrating factor as Q(x) does not exist and i cant seperate so that x and y are separate.

    x.(dy/dx)=-3y + 6x

    some tips please

    What do you mean its not linear? Note that x\frac{\,dy}{\,dx}=-3y+6x \implies \frac{\,dy}{\,dx}+\frac{3}{x}y=6 is of the form \frac{\,dy}{\,dx}+P(x)y=Q(x), which is clearly linear...

    Can you take it from here and use the integrating factor?
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  3. #3
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    thanks..got it now
    i used this before and got the wrong answer..

    integrating factor is e^3lnx
    got answer as y=(3/2)x +c/(x^3)

    which is correct

    thankyou very much
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