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3 May, 06:25

Let y'=4 x. find all values of r such that y = rx^{2} satisfies the differential equation. if there is more than one correct answer, enter your answers as a comma separated list.

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Answers (2)
  1. 3 May, 06:41
    0
    First we solve the differential equation:

    y ' = 4 x

    dy / dx = 4 x

    dy = 4x * dx

    Integrating both sides we have

    int (dy) = int (4x * dx)

    y = 4 (x^2/2)

    y = 2x^2

    Therefore, comparing both functions:

    y = 2x ^ 2

    y = rx ^ 2

    We conclude that

    r = 2

    answer

    The value of r that satisfies the differential equation is

    r = 2
  2. 3 May, 06:52
    0
    Y' = dy/dx = 4x

    To obtain y we integrate wrt x, so y = 4 int (x)

    y = 4 x^2/2 = 2x^2

    But y = rx^2

    So 2x^2 = rx^2

    Comparing coefficients we find that r = 2
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