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Math Help - Verifying Differential Equation

  1. #1
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    Verifying Differential Equation

    The question is read so that y=f(x) is a solution of the given differntial equation

    where y= 1/sqrt(1+x^4)* int (1 to x) sqrt(1+t^4)dt and
    y prime+((2x^3)(y))/(1+x^4)

    I tried solving the integral from 1 to x using substitution u=1+t^4 but i still cant get it... please help me
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  2. #2
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    Quote Originally Posted by dreamx20 View Post
    y prime+((2x^3)(y))/(1+x^4)
    Should that be y prime = 1 + the rest?

    Though, I'm getting y prime = 1 - the rest. Anyway, just in case a picture helps...



    ... where...



    ... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. The right-hand differentiation uses the FTC.

    Edit: here's a neater pic...



    Then, writing the lower integral as the solution for the top one in the top row...



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