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Find a second linearly independent solution given the differential equation & non-trivial solution f.© BrainMass Inc. brainmass.com September 28, 2022, 8:43 pm ad1c9bdddf
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 ...
A second linearly independent solution is found given the differential equation & non-trivial solution f. All work is shown.