Question

solve the D.E dy/dx = (6x^5-2x+1)/(cosy+e^y)

Answer 1

$\frac{dy}{dx}=\frac{6x^5-2x+1}{\cos y +e^y}\\ (\cos y +e^y)dy=(6x^5-2x+1)dx\\ \int(\cos y +e^y)dy=\int(6x^5-2x+1)dx\\ \sin y+e^y=x^6-x^2+x+C.$