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March 27, 2017

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find in implicit form, the general solution of the differential equation

dy/dx = 2(e^x-e^-x)/y^2(e^x+e^-x)^4

  • maths - ,

    The equation is separable.
    After inserting missing parentheses, the equation reads:

    dy/dx = 2(e^x-e^-x)/[y^2(e^x+e^-x)^4 ]
    which can be separated to give:

    y^2 dy = 2(e^x-e^-x)/(e^x+e^-x)^4 dx
    Note that on the right hand side, the numberator is the derivative of the one term of the denominator, which makes for a convenient substitution.
    Integrate both sides:
    y^3/3 = -2/[3(e^x+e^-x)^3]+C

    What's left is to do the algebraic manipulations to yield an explicit form.

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