# Question: find all the independent solutions of the following differential equations...

###### Question details

Find all the independent solutions of the following
differential equations

(a) (1-x^)y"-2xy’+2y=0 (Legendre equation,
n=1)

(b) (x^2)y"+xy'+(x^2)y=0 (Bessel equation, v=0)

(c) (4x^2)y"+4xy'+(4x^2-1)y=0 (Bessel equation,
v^2=1/4)