The differential equation $\frac{dy}{dx} = \frac{7x- 3y-7}{-3x+7y+3}$ reduces to homogeneous form by making the substitution

$x=X+1, y=Y+0$

The correct answer is option (1) : $x=X+1, y=Y+0$

Let $x= X+h, y = Y+k.$ Then, the given equations becomes

$\frac{dY}{dX}=\frac{(7X-3Y)+(7h-3k-7)}{(-3X+7Y)+(-3h+7k+3)}$

This will reduce to a homogeneous differential equation, if

$7h- 3k -7 =0$ and $-3h +7k + 3=0 ⇒h=1, k=0$

Hence, $x=X+1, y=Y+0$ reduces the given equation to homogeneous form.