Show that the equation x (1-x) y (x) + (1 - 5x) y (x) - 4y(x) = 0 has the following linearly independent solutions: y (x) = [ (1+n) x n n=0 too Y(x) = y(x)lu (x1 - 2 n(n+1)x" n=1 Show that the equation (x + x) y " (x) - (x+x) y'(x) + y(x) = 0 has the following lincarly independent solections: y (x) = x (1+x) , 1 Y(x) = y (x) lu|x1 + 1x1 | -2x - 2 --jh y, n=2 n(n-1) X