Consider the ODE (a + bx)y (x) + cxy' (x) + y(x) = 0 in which...

 

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Consider the ODE (a + bx)y" (x) + cxy' (x) + y(x) = 0 in which a, b, c and are constants. a.) (10 points) Determine (in terms of a, b, c and n = 0, 1,2,3,...) how chosen so that one solution to this ODE is a polynomial. = n should be b.) (10 points) Determine the explicate form of the polynomial solution to this ODE for the case when a = 1, b = -4 , c = 4 and = 144, assuming also that this polynomials equals one when x = 1/2. Consider the ODE (a + bx)y" (x) + cxy' (x) + y(x) = 0 in which a, b, c and are constants. a.) (10 points) Determine (in terms of a, b, c and n = 0, 1,2,3,...) how chosen so that one solution to this ODE is a polynomial. = n should be b.) (10 points) Determine the explicate form of the polynomial solution to this ODE for the case when a = 1, b = -4 , c = 4 and = 144, assuming also that this polynomials equals one when x = 1/2.