Solve the constant-coefficient equation in u to find two

Question

We define the linear DE for x > 0:

x²y" + axy' + by = 0.

Use the substitution u = ln(x) to transform the equation to the constant-coefficient equation of the form

d²y/du² + (a - 1) dy/du + by = 0

a. Find a and b.

b. Solve the constant-coefficient equation in u to find two linearly independent solution.

c. Use part (b) to find solution of the DE when a = 1 and b = -1/2. FInd the solution when y(1) = 0 and y'(1) = 1.