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Math Help - quick solution required for DE of TanX*TanY=C?

  1. #1
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    quick solution required for DE of TanX*TanY=C?

    i am very much thankful to the one who show quick solution for DE of TanX*TanY=C?
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  2. #2
    MHF Contributor chisigma's Avatar
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    If I undestand correctly You require the DE the solution of which is, in implicit form,...

    \tan x\cdot \tan\ y = c (1)

    In that case we first separe the variables...

    \tan y= c\cdot \cot x (2)

    ...then compute the logarithm of both sides of (2)...

    \ln \tan y = \ln \cot x + \ln c (3)

    ... then differenziate both sides of (3)...

    \frac{dy}{\tan y\cdot \cos^{2}y}= - \frac{dx}{\cot x\cdot \sin^{2} x} (4)

    ... and finally we obtain...

    y^{'} = -\frac {\sin y\cdot \cos y}{\sin x\cdot cos x}= -\frac{\sin 2y}{\sin 2x} (5)

    Kind regards

    \chi \sigma
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