Calculus

Find the general solution for the differential equation. Leave your solution in implicit form. dx/dt=(2-x)sqrt(1-x)

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  1. dx/dt = (2-x)√(1-x)
    dx/(2-x)√(1-x) = dt

    Note that 2-x = 1 + 1-x = 1 + √(1-x)^2

    2 arctan √(1-x) = t + c
    √(1-x) = tan(t/2 + c) = tan(t/2) + c
    1-x = (tan(t/2) + c)^2
    x = 1 - (tan(t/2)+c)^2

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