Take as given that the x^2 y'' + x'y + x^2.y = 0 has a solution...

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Take as given that the x^2 y'' + x'y + x^2.y = 0 has a solution y1 (x) = Jo (x) = 1 + sum of (at infinity n approaches to 1) (-1)^n x^2n/ 2^2n. (n!)^2 This ODE is known as Bessel's equation and Jo(z) is called the Bessel function of order zero. Take as given that the x^2 y'' + x'y + x^2.y = 0 has a solution y1 (x) = Jo (x) = 1 + sum of (at infinity n approaches to 1) (-1)^n x^2n/ 2^2n. (n!)^2 This ODE is known as Bessel's equation and Jo(z) is called the Bessel function of order zero.

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