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Math Help - Solving differential equations with conditions

  1. #1
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    Solving differential equations with conditions

    y+ 2xy = 0; y= ce^(-x^2); y=0.5 when x = 0

    I have to verify given function is a solution to differential equation. And Find C.

    Help please!

    Thank you.
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  2. #2
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    Red face Re: Solving differential equations with conditions

    Part (i) I guess you'll just have to find y'(x) that should be  C * e^\frac {x^2} {2} * (-2x) .

    So y'(x) =  C * e^\frac {x^2} {2} * (-2x) .

    now find 2yx. You know what y is, so that shouldn't be hard.

    Add both and simplify to get 0.

    This proves that the given function is a solution.

    Part (ii) Next, use the given conditions, y=0.5 when x = 0.

    Just plug the values for x and y in the given equation for y. That should be pretty easy
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