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Math Help - Another DE initial value problem

  1. #1
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    Another DE initial value problem

    Suppose that y=y(x) is a solution of the initial value problem
    y' + e^x y = x^2, y(0) = 4
    Find y'(0) , y''(0)

    So how am I suppose to do the question? I started by doing the integrating factor method but ended up with e^(e^x). So am I on the right track? If not, can someone be kind enough to show me the right way. Many thanks xD
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  2. #2
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    Quote Originally Posted by b4byp4nd4 View Post
    Suppose that y=y(x) is a solution of the initial value problem
    y' + e^x y = x^2, y(0) = 4
    Find y'(0) , y''(0)

    So how am I suppose to do the question? I started by doing the integrating factor method but ended up with e^(e^x). So am I on the right track? If not, can someone be kind enough to show me the right way. Many thanks xD
    Substitute y = 4 when x = 0 into the given DE: y'(0) + e^0 (4) = 0^2 => y'(0) = -4.

    Now differentiate the DE: y'' + e^x y + e^x y' = 2x.

    Substitute y'(0) = -4 and y(0) = 4 and solve for y''.
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