Please see the attached file for the fully formatted problems.
Find a second linearly independent solution given the differential equation & non-trivial solution f.
x^2*y" + 6xy' + 6y' + 6y = 0
x>0, f(x) = 1/x^2
y" + [6(x+1)/x^2]*y' + (6/x^2)y = 0
y" + p(x)y' + q(x) = 0
where p(x) = [6(x+1)/x^2] and q(x) = 6/x^2
Now a second linearly independent ...
A second linearly independent solution is found given the differential equation & non-trivial solution f. All work is shown.