Consider the Chebyshev di↵erential equation (1 x2 )y00 xy0 + 2 y = 0 , where is a constant. Find the power series solutions of this di↵erential equation about x0 = 0. For what values of the constant these solutions reduce to polynomials, known as Chebyshev polynomials. Compute first four of the Chebyshev polynomials

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A: solve x^2y′′−4xy′+ 6y= 0 (not using power series

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.