Multiply both sides by cos(y)/(1+x):
[cos(y)/(1+x)]dy/dx-sin(y)/(1+x)²=1.
Let u=sin(y)/(1+x),
then du/dx=[(1+x)cos(y)dy/dx-sin(y)]/(1+x)²=
[cos(y)/(1+x)]dy/dx-sin(y)/(1+x)², so
du/dx=1 and u=x+C where C is the constant of integration.
Therefore, replacing u, we get:
sin(y)/(1+x)=x+C, sin(y)=(x+C)(x+1)=x²+(1+C)x+C.
y=arcsin(x²+(1+C)x+C).