Answer
$\dfrac{e^y}{2}(\sin y-\cos y)=(x-1)e^x+c$
Work Step by Step
In order to to solve the given differential equation we will have to separate the variables and then integrate.
Here, we have
$\int \dfrac{e^{y}}{\csc y} dy=\int xe^x dx$
or, $\int e^y \sin y dy=\int xe^x dx$
Then, we have $(x-1)e^x+c=\dfrac{e^y}{2}(\sin y-\cos y)$
Hence, $\dfrac{e^y}{2}(\sin y-\cos y)=(x-1)e^x+c$
