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Math Help - Solve the differential equation?

  1. #1
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    Solve the differential equation?

    Solve the differential equation?

    f"(x)=x^2 , f'(0)=6, f(0)=3

    Please help
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  2. #2
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    Consider the rule

     \int x^n ~dx = \frac{x^{n+1}}{n+1}+C

    so

     f'(x) = \int x^2 ~dx = \frac{x^3}{3}+C

    now you must solve for C using f'(0)=6

     f'(x) = \frac{x^3}{3}+C

     6 = \frac{0^3}{3}+C

    now

     C=6 and  f'(x) = \frac{x^3}{3}+6

    Now repeat this step again for  f(x) =\int \frac{x^3}{3}+6~dx using f(0)=3
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