why is dy/dx + sin(dy/dx)=0 not a polnomial function and why its degree is undefined?

Dear student

By definition a polynomial function is a functrion of form f(x) = a_o+a₁x+a₂x²+...+a_nxⁿ

where ais are constants and n is non negative integer.

Now this equation is a differential equation consisting of differential coefficient dy/dx so this not a polynomial function

dy/dx + sin(dy/dx)=0

Hope it clarifies your doubt

Regards

Team Topper