Question

Find two linearly independent solutions of 2x²y" - xy' + (-4x + 1)y = 0, x > 0 of the form

Y₁ = x" (1+ a₁x +а2x² +аzx³ +...)
y₂ = x2 (1+b₁x + b²x² + b²x² + ...)
where ri > T2.
Enter
T1 =
a1 =
a2 =
a3 =
r2 =
b1 =
b2 =
b3 =

Answer 1

2.

Explanation:

T1 = 0

a1 = -1/4

a2 = -1/8

a3 = -1/16

r2 = 1

b1 = 1/2

b2 = 1/8

b3 = 1/48