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Math Help - Newbi here

  1. #1
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    Newbi here

    Im jhay from ph civil engr student can some1 solve this . Get the general solution..

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

    Tnx in advance
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  2. #2
    MHF Contributor
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    Re: Newbi here

    Quote Originally Posted by iamjhay View Post
    Im jhay from ph civil engr student can some1 solve this . Get the general solution..

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

    Tnx in advance
    This is a example of an exact differential equation

    $M(x,y) ~dx + N(x,y)~ dy = 0$

    $M(x,y)=\Phi_x(x,y)$

    $N(x,y)=\Phi_y(x,y)$

    where $\Phi(x,y)$ is to be determined.

    $M_x(x,y)=2xy+x^2+x^4$

    $\Phi(x,y)=x^2y+\dfrac {x^3}{3}+\dfrac{x^5}{5}+f(y)$

    $\Phi_y(x,y)=x^2 + \dfrac{df}{dy}(y) = N(x,y)=1+x^2$

    $\dfrac{df}{dy}(y)=1$

    $f(y)=y+C$

    $\Phi(x,y)=x^2y+\dfrac {x^3}{3}+\dfrac{x^5}{5}+y+C=(1+x^2)y+\dfrac {x^3}{3}+\dfrac{x^5}{5}+C$
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