9. Consider the differential equation x2 ay = 2 - 4xy + xy on the interval (0, co). (a) Determine the value(s) of c so that y1 (x) = - is a solution to the above differential equation. Solve the differential equation. A . ) . x 2 CY - 2 + 4 x y - x 2y 2 = 0 ) . Y(x) = S LY = - *(- * ) - 2+4x(* )-X"( *)?= 0 - ( - 2 + 4 6 - (2 = 0 -> - ((2 + (-46+ 2) = 0->-(2- 36+2)=0 - LL-1) (1- 2) = 0- . Values : C = 1, 2 let 4 , (x ) = I -B. ) . 12 ( x )= 2 dx x249 = 2 - 4xy + x2y' 43 ( x ) = u (x ) x2 8 - 2 = - Y(4x - x2y) where solution giftz x t u = * f U . du dy = -3 dx X - ( y ) + yz 3 = * 2 - x 3 + u ) + ( 2 + 4 ) 2 du 12 X2 - 49 + X du = x z + z u tu 2 * 2 = - 4 + 2xu txu 2