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Thread: 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

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

    so

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

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

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

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

    now

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

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