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  4. The solution of the equation (dy/dx) = (3x - 4y - 2/3x - 4y - 3)

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Q. The solution of the equation $\frac{dy}{dx} = \frac{3x - 4y - 2}{3x - 4y - 3}$

Differential Equations

Solution:

Put $3x -4y = X$
$ \Rightarrow 3-4 \frac{dy}{dx} = \frac{dX}{dx} \Rightarrow \frac{dy}{dx} = \frac{1}{4} \left(3- \frac{dX}{dx}\right) $
$\Rightarrow \frac{3}{4} - \frac{1}{4} \frac{dX}{dx} = \frac{X-2}{X-3} $
$\Rightarrow - \frac{1}{4} \frac{dX}{dx} = \frac{4X - 8 -3\left(X -3\right)}{4\left(X-3\right)} $
$= - \frac{1}{4} \frac{dX}{dx} =\frac{X+1}{4\left(X-3\right)} $
Now, solve it.
Required solution is x - y + c = log (3x - 4y + 1)