Consider the differential equation xy + y = y = 0 - (a) The point x = 0 is = a regular singular point

Consider the differential equation $y\"+y'y=0 (a) The point a: : 0 is a regular singular pointy (b) Find the exponents at the singular point :6 = 0. (c) Find two solutions of the differential equation (not multiples of each other) about a: = 0. If one of the solutions (found for 0,0 = 1) is: W) = then a second solution is: NOTE: Enter the rst four nonzero terms of the expansion. momm (a) The point x = 0 is a regular singular (b) Find the Choose one ar po 1 1 + (n!) 2 0n (c) Find two n=1 tial (not mult ut x If one of 1 - (( n + 1 )!) 2 a = n= y1 (20) = 1 1 - (n!) ? an n=1 then a se NOTE: En ( - 1) " of th 1 + (n!) 2 on y2 (20) = y n=0 1 1 + n= ( (n + 1 ) !) 2

Consider the differential equation xy" + y = y = 0 - (a) The point x = 0 is = a regular singular point (b) Find the exponents at the singular point x = 0. r1 = r2 = (c) Find two solutions of the differential equation (not multiples of each other) about x = 0. If one of the solutions (found for ao = 1) is: 31(2) = Choose one then a second solution is: NOTE: Enter the first four nonzero terms of the expansion. Y2(x) = y(x) ln x+