The degree of the differential equation sin (dy/dx)=x+y is

The degree is defined only when the equation is a polynomial in the derivatives. Here $\frac{dy}{dx}$ appears inside the transcendental function $\sin$, so the equation cannot be written as a polynomial in $\frac{dy}{dx}$, and the degree is not defined (the order is $1$). The tempting answer $1$ confuses order with degree.