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Unformatted text preview: n 1 2 2 x x b x ln x Cy x y ; b Note: For this case we have a possibility that the second solution may have C = This would give 2 series solutions, but we have no way of knowing this before we have solved the ODE completely Case 3: Roots are equal 2 1 2 1 r r r r = =-Two solutions exist: ( 29 ( 29 = +-= n r n n 1 1 x x c x y ; c and ( 29 ( 29 ( 29 = +-+ = n r n n 1 2 2 x x b x ln x y x y Note: The log term always occurs in this case. Finding the second solution: We can use Reduction of Order to find the second solution....
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- Fall '08