Calculus

Find y that satisfies the given condition

dy/dx=20x(5x^2-1)^3; curve passes through (1,3)

I took the antiderivative and ended up with 10x^2((5x^2-1)^4/4). I end up with a large number at the end, which I think might be wrong.

asked by Mike
  1. let
    u = 5x^2-1
    du = 10x dx

    so, what you have is 2u^3 du
    y(x) = u^4/2 = 1/2 (5x^2-1)^4 + C
    y(1) = 3, so
    1/2 (5-1)^4+C = 3
    2C = 6-256 = -250

    y(x) = 1/2 (5x^2-1)^4 - 125

    Had you checked your function, you would have seen that its derivative was not the original dy/dx.

    posted by Steve

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