Unformatted text preview: tude. Identical real roots If the roots are real and equal, i.e., r = s , then the solution becomes y n = ( c 1 + c 2 ) r n = c 3 r n But if c 3 r n is a solution, then so is c 4 nr n (see Chiang 1992, p. 580 or Goldberg 1961, p. 136 and exercise 14), hence the general solution when the roots are equal is given by y n = c 3 r n + c 4 nr n We can now solve for c 3 and c 4 given the two initial conditions y and y 1 y = c 3 r + c 4 (0) r = c 3 y 1 = c 3 r + c 4 (1) r = ( c 3 + c 4 ) r...
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- Fall '11
- Economics, Trigraph, yn, Order theory, Monotonic function, Convex function