Question

One solution of the Chebyshev equation



1 − x

2

-



y

′′ − xy′ + n

2

y = 0

for n = 0 is y1 = 1.

(a) Using Eq. (9.127), develop a second, linearly independent solution.

(b) Find a second solution by direct integration of the Chebyshev equation.

Hint. Let v = y

′

and integrate. Compare your result with the second solution given in

Section 13.3.

ANS. (a) y2 = sin−1

x.

(b) The second solution, Vn(x), is not defined for n = 0.​

Answer 1

Answer:

B) x2 =sin-5

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