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Math Help - Helpe-me

  1. #1
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    Helpe-me

    Boa tarde, poderiam me ajudar a resolver a seguinte Equação ?


    Por favor postem os passos , Desde já agradeço..


    a) Resolva a seguinte equação

    y"=x(y')²
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  2. #2
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    Re: Helpe-me

    $y^{\prime\prime}=x(y^\prime)^2$

    $u=y^\prime$

    $u^\prime = x u^2$

    $\dfrac {du}{u^2} = x~dx$

    Spoiler:
    $-\dfrac 1 u=\dfrac 1 2 x^2 + C_1=\dfrac{x^2+C}{2}$

    $u=-\dfrac 2 {x^2+C}$

    $y'=-\dfrac 2 {x^2+C}$

    $y=-\sqrt{\dfrac 2 C}\arctan\left(\dfrac{x}{\sqrt{2C}}\right)+D$
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  3. #3
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    Re: Helpe-me

    desculpa, ainda não intendi ... poderia me explicar quem você chamou de U os passos todos . por favor ..
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  4. #4
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    Re: Helpe-me

    como que fica a resposta final ?

    só para conferir com a minha ..
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  5. #5
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    Re: Helpe-me

    Quote Originally Posted by SIDNEYFERNANDO View Post
    como que fica a resposta final ?

    só para conferir com a minha ..

    u is just a name I gave to y' to make things clearer.
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