There are often several ways to write a function. But it seems to me that your S2 solutions are not independent.
syms y(x) C1
S1 = dsolve(diff(y)==y+sin(x))
S2 = -1/2*cos(x)-1/2*sin(x)+exp(x)*C1
res1 = simplify(diff(S1,x)-S1-sin(x))
res2 = simplify(diff(S2,x)-S2-sin(x))
S1 = dsolve((diff(y))^2+y^2==1)
S2 = [sin(x-C1) ;-sin(x-C1)]
res1 = simplify(diff(S1,x).^2+S1.^2-1)
res2 = simplify(diff(S2,x).^2+S2.^2-1)
