1. The 2nd order Cauchy-Euler equation is given by xy (x)+axy' (x) + by(x) = 0,...

  

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1. The 2nd order Cauchy-Euler equation is given by xy" (x)+axy' (x) + by(x) = 0, x>0, a, b R. (a) Derive the two values of r = 11, 12 (in terms of a and b) that would enable Y = to be a solution of (1). (1) X" (b) Derive the general solution, y = (x) + 2u2(x), of () if r and r2 are equal, simplifying your solution where possible. 1. The 2nd order Cauchy-Euler equation is given by xy" (x)+axy' (x) + by(x) = 0, x>0, a, b R. (a) Derive the two values of r = 11, 12 (in terms of a and b) that would enable Y = to be a solution of (1). (1) X" (b) Derive the general solution, y = (x) + 2u2(x), of () if r and r2 are equal, simplifying your solution where possible.