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Math Help - dif equations

  1. #1
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    dif equations

    Hi all

    which method do i use to solve this:
    Attached Thumbnails Attached Thumbnails dif equations-111.gif  
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  2. #2
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    Quote Originally Posted by moolimanj View Post
    Hi all

    which method do i use to solve this:
    Integrating factor method.

    But I'd first re-arrange into: \frac{dy}{dx} + \frac{2}{x} \, y = \frac{5}{x^3}.

    Hint: The integrating factor is e^{\int \frac{2}{x} \, dx} = e^{2 \ln x} = e^{\ln x^2} = x^2.
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  3. #3
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    sorry to butt in..but I want to understand differential equations better, if you use the integrating factor do you multiply by all the terms? how would you proceed from here?
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    Quote Originally Posted by dankelly07 View Post
    sorry to butt in..but I want to understand differential equations better, if you use the integrating factor do you multiply by all the terms? how would you proceed from here?
    Multiply both sides by x^2. That's the only way to make sure the equation still says the same thing.
    \frac{dy}{dx} + \frac{2}{x} \, y = \frac{5}{x^3}

    x^2 \cdot \frac{dy}{dx} + x^2 \cdot \frac{2}{x} \, y =  x^2 \cdot  \frac{5}{x^3}

    x^2 \cdot \frac{dy}{dx} + 2xy =  \frac{5}{x}

    \frac{d}{dx} \left ( x^2y \right ) = \frac{5}{x}

    Now integrate both sides with respect to x:
    x^2y = 5~ln(x) + C

    You take it from here.

    -Dan
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