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10. The Chebyshev Equation. The Chebyshev differential equation is(1 - x^2)y” - xy' α^2y = 0,where α is a constant.(a) Determine two solutions in powers of x for |x| < 1, and show that they form afundamental set of solutions.(b) Show that if α is a nonnegative integer n, then there is a polynomial solution ofdegree n. These polynomials, when properly normalized, are called the Chebyshevpolynomials. They are very useful in problems that require a polynomial approximationto a function defined on

10. The Chebyshev Equation. The Chebyshev differential equation is(1 - x^2)y” - xy' α^2y = 0,where α is a constant.(a) Determine two solutions in powers of x for |x| < 1, and show

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