This problem is a very simple example of a differential equation: an equation that relates a function to one or more of its derivatives. You

Question

This problem is a very simple example of a differential equation: an equation that relates a function to one or more of its derivatives. You can solve this problem by doing some educated guessing. (“educated” means “remember what we did in the past.”) Suppose f is the function that satisfies f(x)-fx) for all T in its domain, and Then f(x) =___________

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Lệ Thu 3 years 2021-09-05T05:57:25+00:00 1 Answers 228 views 0

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  1. Philomena
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    2021-09-05T05:59:02+00:00
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    Answer:

    f(x) = 1/x

    Step-by-step explanation:

    The corrected question is:

    Suppose f is the function that satisfies  

    f'(x)= – f²(x)  

    for all x in its domain, and  

    f(1) = 1  

    f(x)= ?

    Given:

    f'(x) = -(f(x))²

    This can be written as:

    df/dx = -f²

    The equation becomes:

    -df/f² = dx

    Integrating the above equation on both sides we get:

    1/f = x + c     where c is constant

    So

    f(x) = 1/(x+c)

    Now given that:

    f(1) = 1  

    Solving this for c we get:

    f(1) = 1 = 1/(1 + c)

    1 = 1/ 1+c  

    1 = 1 + c

    c = 1 – 1

    c = 0

    Now put this value of c in f(x) = 1/(x+c)

    f(x) = 1/(x+0)

    f(x) = 1/(x)

    f(x) = 1/x

    Hence

    f(x) = 1/x

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