Question

The solution of differential equation coty dx=x dy is ______ .

Answer 1

Given differential equation is
coty dx=x dy
$\Rightarrow \frac{1}{x}dx=tanydy$
On integrating both sides, we get
$\Rightarrow \int \frac{1}{x}dx=\int tanydy\Rightarrow log\left(x\right)=log\left(secy\right)+logC\Rightarrow log\left(\frac{x}{secy}\right)=logC\Rightarrow \frac{x}{secy}=C\Rightarrow x=Csecy$