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Math Help - differential eq, conditions

  1. #1
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    differential eq, conditions

    dy/dx = (x*e(to pwr of y) )/ x(to pwr of 2) + 1
    given conditions y=0 at x=0.
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  2. #2
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    \frac{dy}{dx}=\frac{xe^{y}}{x^{2}+1}\implies e^{-y}\,dy=\frac{x}{x^{2}+1}\,dx.

    Can you take it from there?
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  3. #3
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    \frac{dy}{dx} = \frac{xe^y}{x^2+1}

    separate variables ...

    e^{-y} \, dy = \frac{x}{x^2+1} \, dx

    do the integration.
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  4. #4
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    Quote Originally Posted by Krizalid View Post
    \frac{dy}{dx}=\frac{xe^{y}}{x^{2}+1}\implies e^{-y}\,dy=\frac{x}{x^{2}+1}\,dx.

    Can you take it from there?
    Is that separation of variables now? Hm, so we get I of e to -y = I of right side, right?
    Not sure, am new to this... thx for help.
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  5. #5
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    Yes, and don't forget the constant.
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  6. #6
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    Quote Originally Posted by Krizalid View Post
    Yes, and don't forget the constant.
    I get e to -y = 1/2 log (x2 +1 ) + c

    So -y = log (1/2 log (x2 + 1) +c ) and y=-log of said? Afraidn i messed smth again...
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