1. Given the following differential equation y" – xy' = 0. (a) Show that the general solution of the differential equation above about r = 0 is 22n+1 y = ao + a1 > 2" (2n + 1)n!" n=0 [Hint: 2 x 4 x...

Please refer to the image below, solve by using power series method

2" (2n + 1)n!" n=0 [Hint: 2 x 4 x ·.x 2n = 2"n!] (b) Find the specific solution if y(0) = 1 and y' (0) = 2. "/>
Extracted text: 1. Given the following differential equation y" – xy' = 0. (a) Show that the general solution of the differential equation above about r = 0 is 22n+1 y = ao + a1 > 2" (2n + 1)n!" n=0 [Hint: 2 x 4 x ·.x 2n = 2"n!] (b) Find the specific solution if y(0) = 1 and y' (0) = 2.