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Please suggest appropriate substitution to reduce it to separable form

$\frac{dy}{dx} = \frac{4x+7y+2}{4x+7y+3} $

let $z=4x+7y$ then $\frac{dz}{dx}=4+7\frac{dy}{dx}$ $ \frac {dy}{dx}= \frac17 (\frac{dz}{dx}-4) $ $\frac 17 (\frac {dz}{dx}-4) = \frac {z+2}{z+3}$ please help further now i need the value of $\frac {dz}{dx}$

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Let $u=4x+7y$, now we get: $du/dx=4+7dy/dx$

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    @TPSstar: See my second comment abo$v$e and do the same with that substitution again.2012-11-15