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Math Help - ODE

  1. #1
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    ODE

    i am refreshing my knowledge and theory on ode's and i have noticed that i have pretty much forgotten a lot of stuff.
    Can some one give me a few pointers for making substitutions for solving non linear first order and second order sdes

    Eg y(x)=y(x)^2
    y(0)=1
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  2. #2
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    Re: ODE

    Quote Originally Posted by johnnys View Post
    i am refreshing my knowledge and theory on ode's and i have noticed that i have pretty much forgotten a lot of stuff.
    Can some one give me a few pointers for making substitutions for solving non linear first order and second order sdes

    Eg y(x)=y(x)^2
    y(0)=1
    What you have written is not a DE.

    Did you mean \displaystyle \begin{align*} \frac{dy}{dx} = y^2 \end{align*}?
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    Re: ODE

    yeah its supposed to be y'=y^2
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    Re: ODE

    Quote Originally Posted by johnnys View Post
    yeah its supposed to be y'=y^2
    That equation is separable.

    \displaystyle \begin{align*} \frac{dy}{dx} &= y^2 \\ y^{-2}\,\frac{dy}{dx} &= 1 \\ \int{y^{-2}\,\frac{dy}{dx}\,dx} &= \int{1\,dx} \\ \int{y^{-2}\,dy} &= \int{1\,dx} \end{align*}

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