- 10

- 0

Can anyone tell me if I'm on the right track and if I've done these steps right so far? Also, what do I need to do next because I'm not sure how I know if I have 3 linearly independent solutions?y^(3) + 3y'' + 3y' + y = 0

r^2(r+3) + 3r + 1 = 0

r=0 of degree 2

r=-3 of degree 1

r=-1/3 of degree 1

y(x)=c1 + c2x + c3(e^(-3x)) + c4(e^((-1/3)x))