Using Mathematica: Determine whether the given set of functions are linearly dependent or independent on (-,):

1. f₁(x) = x^-2, f₂(x) = x³, f₃(x) = x³ ln(x)

2. f₁(x) = Cos(2x), f₂(x) = Sin(2x), f₃(x) = Cos(x)Sin(x)

3. f₁(x) = ^x , f₂(x) = ^-x , f₃(x) = Sinh(x)

4. f₁(x) = Cos(2x), f₂(x) = x, f₃(x) = Cos²(x), f₄(x) = Sin(2x)

5. Given the Nonhomogeneous DE: 2x² y'' + 5xy' + y = x² - x

General Sol'n: y = C₁x^(-1/2)+ C₂x^-1 + (1/15)x²- (1/6)x on (0, )

a. Show linearly independent for the complimentary solution.

b. Show that y is a solution to the DE by using DSolve.