Question

To find the general solution of $si{n}^{-1}\left(\frac{dy}{dx}\right)=x+y$ using variable separable method, the substitution to be used is .

• A. $v=\frac{y}{x}$
• B. $v=yx$
• C. $v=x+y$
• D. $v=x-y$

Answer 1

The correct option is C $v=x+y$

Here, the differential equation is $si{n}^{-1}\left(\frac{dy}{dx}\right)=x+y$
$\therefore \frac{dy}{dx}=sin(x+y)$. Since (x+y) occurs together at a term, let's make the substution $v=x+y$.
On differentiating w.r.t x, $\frac{dv}{dx}=1+\frac{dy}{dx}$
Based on this, the original DE reduces to $\frac{dv}{dx}-1=sinv$ which is of the variable separable form.