Is the differential equation y′=x+y+sin(x)y' = x + y + \sin(x)y′=x+y+sin(x) linear?
Yes, because all terms involving yyy and y′y'y′ are of degree 1.
No, because sin(x)\sin(x)sin(x) is not a linear function of xxx.
No, because xxx is present.
Yes, but only for y=0y=0y=0.