calculus

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find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)

  • calculus -

    dy/dx = 3xy
    dy/y = 3x dx
    ln y = 3x^2/2+c
    y = Ce^3x^2/2

    2 = Ce^0
    C = 2

    y = 2e^(3x^2/2)
    y' = 2e^(3x^2/2)*(3x)
    = 3xy

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