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Math Help - Differential Equation

  1. #1
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    Differential Equation

    Find if satisfies

    and the -intercept of the curve is .

    The f(x) and y and x are all mixing me up. I tried doing...

    1/34 \int 1/y  dy = \int x^{16}dx

    and solved for y getting...

    y = e^{2x^{17} + 136 + C}

    But i don't understand how to find C because of all the f(x), y, etc. Then i would have to change it back to f(x) somehow...
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  2. #2
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    Quote Originally Posted by twoteenine View Post
    But i don't understand how to find C because of all the f(x), y, etc. Then i would have to change it back to f(x) somehow...
    This part is telling you to use the point (0,4) in your answer for y to solve for C.
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  3. #3
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    Quote Originally Posted by twoteenine View Post
    Find if satisfies

    and the -intercept of the curve is .

    The f(x) and y and x are all mixing me up. I tried doing...

    1/34 \int 1/y  dy = \int x^{16}dx

    and solved for y getting...

    y = e^{2x^{17} + 136 + C}

    But i don't understand how to find C because of all the f(x), y, etc. Then i would have to change it back to f(x) somehow...
    I've not checked your integration so it may be wrong. To find C use the fact you're given the y intercept.

    At the y intercept we get (0,4). Sub this into the equation

    To make life easier I'm going to use k such that k = e^C

    4 = k \cdot e^{2(0)^{17}+136}

    Solve for k
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