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CALCULUS

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Using the separation of variables technique, solve the following differential equation with initial condition:
(4x sqrt)(1 - t^2)(dx/dt) - 1 = 0 and x(0)=-2
I believe that the answer is one of the following two options:
a.) 2x^2 = arcsint + 8
b.) arccost + 8 - (1/2)pi

  • CALCULUS -

    4 x dx = dt/sqrt (1-t^2)
    2 x^2 = sin^-1 (t) + c
    when t = 0, x = 2
    8 = 0 + c
    c = 8
    so 2 x2 = sin^-1 (t) + 8
    or
    2 x^2 = cos^-1(t) + c
    8 = pi/2 + c
    yes, agree

  • CALCULUS -

    I'm only permitted to choose one option. And seeing as you came up with arcsin first, would this be a better answer over the option with arccos?

  • CALCULUS -

    They are the same.
    cos (pi/2 - x) = sin x

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