need help with linear differential equation?

Solve this differential equation by using an integrating factor:

(1 - x²)(dy / dx) - x²y = (1 + x)√(1 - x²)

dy / dx - x²y / (1 - x²) = (1 + x) / √(1 - x²)

dy / dx + x²y / (x² - 1) = (1 + x) / √(1 - x²)

P(x) = x² / (x² - 1)

f(x) = (1 + x) / √(1 - x²)

I(x) = ℮^[∫ P(x) dx]

I(x) = ℮^[∫ x² / (x² - 1) dx]

I(x) = ℮^[∫ {1 - 1 / (1 - x²)} dx]

I(x) = ℮^(x - tanhˉ¹x)

I(x)y = ∫ I(x)f(x) dx

y℮^(x - tanhˉ¹x) = ∫ (1 + x)℮^[x - tanhˉ¹x] / √(1 - x²) dx

y℮^(x - tanhˉ¹x) = ∫ ℮˟ dx

y℮^(x - tanhˉ¹x) = ℮˟ + C

y℮^(x - tanhˉ¹x) = C + ℮˟

y = (C + ℮˟) / ℮^(x - tanhˉ¹x)

wolframalpha.com

http://www.wolframalpha.com/input/?i=%281-x^2%29dy...

They won't tell you how they got it, but there it is.

i know you can do it, just believe it yourself! :))