Question

The solution of $\frac{dy}{dx}+1=\csc (x+y)$ is

• A. $\cos (x+y)+x=c$
• B. $\cos (x+y)=c$
• C. $\sin (x+y)+x=c$
• D. $\sin (x+y)+\sin (x+y)=c$

Answer 1

The correct option is A $\cos (x+y)+x=c$

Given, $\frac{dy}{dx}+1=\csc (x+y)$
Put $x+y=t$
On differentiating with respect to $x$, we get
$1+\frac{dy}{dx}=\frac{dt}{dx}$
$\therefore \frac{dt}{dx}=\csc t$
$\Rightarrow \sin tdt=dx$
On integrating, we get
$-\cos t=x-c$
$\cos t+x=c$
$\Rightarrow \cos (x+y)+x=c$