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calculus

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find the general solution to the differential equation.
dy/dx=secxtanx-e^x

  • calculus -

    The equation is separable, meaning that we can put x and y on each side of the equal sign.

    dy/dx=secxtanx-e^x
    =>
    dy = (sec(x)tan(x) - e^x)dx

    Integrate both sides:

    ∫dy = ∫(sec(x)tan(x) - e^x)dx
    =>
    y = sec(x)-e^x + C
    where C is an integration constant.

    differentiate the above solution to confirm that the solution is correct.

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