Can you explain why (a) a solution of r*y" + xy' + (x² – µ²)y = 0 (1) is of the form y(x) = E Anx"+r %3D n=0 (b) a solution of (1 – x²)y" – 2xy' + l(1 + 1)y = 0 (2) is of the form y(x) = Lana". %3D...

Extracted text: Can you explain why (a) a solution of r*y" + xy' + (x² – µ²)y = 0 (1) is of the form y(x) = E Anx"+r %3D n=0 (b) a solution of (1 – x²)y" – 2xy' + l(1 + 1)y = 0 (2) is of the form y(x) = Lana". %3D n=0 Can you state in few words three types of resemblance between the differ- ential equations (1) and (2).