The differential equation
$\frac{d y}{d x}=\frac{7 x-3 y-7}{-3 x+7 y+3}$
reduces to homogeneous form by making the substitution
Answer & explanation
Correct answer: option 1
Let $x=X+h, y=Y+k$. Then, the given equation. becomes
$\frac{d Y}{d X}=\frac{(7 X-3 Y)+(7 h-3 k-7)}{(-3 X+7 Y)+(-3 h+7 k+3)}$
This will reduce to a homogeneous differential equation, if
$7 h-3 k-7=0$ and $-3 h+7 k+3=0 \Rightarrow h=1, k=0$
Hence, $x=X+1, y=Y+0$ reduces the given equation to homogeneous form.