The differential equation $\frac{dy}{dx} = \frac{x+y-1}{x+y+1}$ reduces to variable separable form by making the substitution
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : $x+y = v$
Let $x+y=v$. Then, $1+\frac{dy}{dx} =\frac{dv}{dx}.$
Substituting these values in the given differential equation,
we get
$\frac{dv}{dx}-1=\frac{v-1}{v+1}$
$⇒\frac{dv}{dx}=\frac{2v}{v+1}$
$⇒\frac{v+1}{2v}dv=dx$
Clearly, it is in variable separable form.