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separatio of variables

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solve the initial value problem by separation of variables dy/dx=6x^2y and y(0)=4

  • separatio of variables - ,

    ydy=6x^2 dx

    y^2/2=2x^3 + C

    y(0)=4
    16/2=C

  • separatio of variables - ,

    dy/y = 6 x^2 dx
    ln y = 2 x^3 + c

    when x = 0, y = 4
    ln 4 = c
    so
    ln y = 2 x^3 + ln 4

    ln (y/4) = 2 x^3

    or
    y/4 = e^(2x^3)
    y = 4 e^(2x^3)

  • separatio of variables - ,

    damon is correct, I lost y.

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