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Math Help - Differential Equation

  1. #1
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    Differential Equation

    Hey

    Im trying to solve the following differential equation.

    x*dy/dx +y = e^(-x) <--- e (to the power of) -x

    But I can't rearrange the equation to get the x's on the left handside and the y's on the right hand side

    can somebody please help me out

    Thanks a million

    Eddie
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  2. #2
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     <br />
xy'+y=e^{-x}.

    This is a linear ODE, but instead to find the integrating factor, we can see that xy'+y=(x\cdot y)'=e^{-x}\implies xy=\int e^{-x}\,dx.

    Can you take it from there?
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  3. #3
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    Im not really familar with linear DE's

    but i got this answer

    y=x(-(1/x*e^x))+(c/x)

    Am i on the right track?
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  4. #4
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    I don't get very well what you wrote, but the answer is y(x)=\frac{k-e^{-x}}x.
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  5. #5
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    Ok think I'm doing it wrong could you please show me your working ? Would help me heaps

    Much Appreciated

    Eddie
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  6. #6
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    Since \int e^{-x}\,dx=-e^{-x}+k,

    xy=-e^{-x}+k, and the conclusion follows.
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  7. #7
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    Hey again

    I dont quiet understand what you did? This basically what Im doing.

    x*(dy/dx) + y = e^-x

    d(xy)/dx = e^-x

    d(xy) = (e^-x) dx

    xy = -e^-x + c

    y = (1/x)*(-e^-x + c)

    Is this right? if not where am I going wrong?
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  8. #8
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    It is correct, it's just that on post #3 I didn't understand the notation.

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