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Math Help - differential equation

  1. #1
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    differential equation

    help me solve this differential equation
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  2. #2
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    Quote Originally Posted by carlasader View Post
    help me solve this differential equation
    5. The ODE:

    (x+1)y \frac{dy}{dx}+1=0

    is of variables seperable type, so rewrite as:

     <br />
y \frac{dy}{dx}= -~\frac{1}{x+1}<br />

    so:

     <br />
\frac{d}{dx} \left( \frac{y^2}{2} \right)=-~\frac{1}{x+1}<br />

    RonL
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  3. #3
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    Quote Originally Posted by carlasader View Post
    help me solve this differential equation
    6. The normal to the curve x=2/t, y=2t at a point has slope -1/(dy/dx)

    Now:

     <br />
\frac{dy}{dx}=\frac{dy}{dt}~\frac{dt}{dx}=(2)\left  (-\frac{2}{x^2}\right)<br />

    So now you know the point, and the slope of the normal at that point, so you
    can find the equation of the normal

    RonL
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  4. #4
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    Quote Originally Posted by carlasader View Post
    help me solve this differential equation
    5)
    (x+1)y\frac{dy}{dx} + 1 = 0

    (x+1)y\frac{dy}{dx} =  -1

    y\frac{dy}{dx} =  -\frac{1}{x+1}

    y dy =  -\frac{dx}{x+1} and so on...

    7)
    Since the slope is 2 and we know the equation of a line is of the form y = (slope)x+(y-intercept)
    So its of the form y = 2x+c
    Since (2,5) is on the line, we have 5 = 2(2) + c \Rightarrow c = 1
    So y = 2x + 1.

    y = 0 \Rightarrow x = -\frac{1}2
    x = 0 \Rightarrow y = 1
    So the mid point of (0,1) and \displaystyle (-\frac{1}2, 0) is \displaystyle (-\frac{1}4, \frac12)
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by carlasader View Post
    help me solve this differential equation
    Don't post multiple questions like this in the same thread. Posting them in a
    single thread makes it less likely that you will get help will all of them.

    RonL
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