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Math Help - differentiation

  1. #1
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    differentiation

    if the graph of y=f(x) contains the point (0,2), dy/dx=-x/ye^(x^2) and f(x)>0 for all x then f(x) = ?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by lbj2322 View Post
    if the graph of y=f(x) contains the point (0,2), dy/dx=-x/ye^(x^2) and f(x)>0 for all x then f(x) = ?
    y'=-\frac{x}{ye^{x^2}} \implies yy' = -\frac{x}{e^{x^2}}

    Integrate both sides. (Use u-substitution with u=x^2 and du=2x\,dx on the righthand integral.)

    \int yy'\,dx = -\int\frac{x}{e^{x^2}}\,dx \implies \frac{1}{2}y^2 = \frac{1}{2}e^{-x^2}+c \implies y = \sqrt{e^{-x^2}+C}

    Plug in (0,2): 2=\sqrt{1+C} \implies C=3

    So y=f(x)=\sqrt{e^{-x^2}+3}
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  3. #3
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    thanks alot

    i was confused on what to do with the coordinates but now i understand. Thanks again
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