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Math Help - Help in solving a Differential Equation

  1. #1
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    Help in solving a Differential Equation

    Solve  \frac{dy}{dx} = \frac{x+ytany}{y-xtany}
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  2. #2
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    First write your ODE as

    (x + y \tan y)dx +(x \tan y - y)dy = 0 then as

    (x \cos y + y \sin y)dx +(x \sin y - y \cos y)dy = 0

    which is of the form

    M(x,y)dx + N(x,y)dy = 0. Then check \dfrac{M_y-N_x}{N}

    If \dfrac{M_y-N_x}{N} = Q(x) then \mu = e^{\int Q(x)dx} is an integrating factor.
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  3. #3
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    Hi,

    Thank you for your post! Is there any way I can do this problem without resorting to Integrating Factors? I'm just curious, the problem suggests you take  \frac{x}{y} = \tan{\theta}  , I tried doing that to no avail.
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