Question

Q: 1 The equation y" + y'-xy =0 has a power series of the form
y = Summation from n = 0
to n ::a(n)x^n

i ) Find the Power series solutions
y1(x) and y2(x) such that y1(0) = 1 ,
y1'(0)= 0 and y2(0) = 0 , y2'(0) = 1


ii ) Find the radius of convergence
for y1(x) and y2(x) .

For better clarity see pic uploaded.

Answer 1

Understanding :

1) Analytic functions
2) Power series solution.


Hope, you understand my solution and it may helps you.