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Math Help - general solution of differential equation (express y in term of x)

  1. #1
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    general solution of differential equation (express y in term of x)

    i got stucked here. below is the answer given. can anybody help please?general solution of differential equation (express y in term of x)-dsc_0143-7-1-.jpggeneral solution of differential equation (express y in term of x)-dsc_0143-6-1-.jpg
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  2. #2
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    Re: general solution of differential equation (express y in term of x)

    I have no idea what you are trying to do here!

    First, I would write the equation as \frac{dy}{dx}+ 2\frac{y}{x}= 2 tan^{-1}(x)
    This is a linear equation so there is a standard formula for the "integrating factor", a function, v(x), so that multiplying by it will make the left side an "exact derivative": v(\frac{dy}{dx}+ 2\frac{y}{x})= v\frac{dy}{dx}+ 2v\frac{y}{x}= \frac{dvy}{dx}= 2tan^{-1}(x).

    This leads to an integral that looks difficult if not impossible to integrate with elementary functions so you may have to write the function with an indicated integration.
    Last edited by HallsofIvy; May 3rd 2014 at 07:42 AM.
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    Re: general solution of differential equation (express y in term of x)

    general solution of differential equation (express y in term of x)-dsc_0145-3-2-.jpgi redo the question but how to integrate arc tan x ?Click image for larger version. 

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