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Thread: Integrate second order differential equation

  1. #1
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    Integrate second order differential equation

    I need to integrate the function d^2 y/d x^2=0

    I know I need to begin by...

    d^2 y/d x^2 =

    d/dx * dy/dx =

    d/dy * dy/dx * dy/dx

    .... after that I am lost.
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  2. #2
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    How did you get from one step to the other?

    Quote Originally Posted by cheme View Post

    d/dx * dy/dx =

    d/dy * dy/dx * dy/dx
    Are you trying to find y?
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  3. #3
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    Yes I am trying to find y. However, I just tried to factor out differentials. I am confused because there is nothing else to go along with the equation, thus preventing me from using any DiffEq technique.
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  4. #4
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    Do this...

    d^2y/dx^2=0

    dy/dx=A where A= constant

    y=Ax+b where B = constant..

    hence y=Ax+b

    This satisfies the given differential
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  5. #5
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    You are trying to get?

    \frac{d^2y}{dx^2} = 0

    \frac{d}{dx} \frac{dy}{dx} = 0

    \frac{d}{dx} \frac{d}{dx} (y) = 0

    Maybe then intgrate twice on both sides?

    y = \int \int 0 ~dx~dx
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  6. #6
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    The final answer should relate y to x.

    I know the final answer is y=(y2-y1)(x-x1)/(x2-x1) +y1
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  7. #7
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    Cheme: It's effectively the same thing

    y=(y2-y1)(x-x1)/(x2-x1) +y1 = Ax+b

    where A= y2-y1/x2-x1 and B=((y2-y1)*x1/x2-x1) +y1

    They gave you the solution in general form with gradient and everything from y-y1=m(x-x1) form..

    All I did is say

    y''(x)=0 --> y'(x)=A -->y(x)=Ax+B where A,B are constant..
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