Question: 9. Solve completely using operator methods: (a) y(5) + 2y (3) = 30 + e-5x (b) (D + 3) y = e- 3 sin x

9. Solve completely using operator methods: (a) y(5) + 2y (3) = 30 + e-5x (b) (D + 3) y = e- 3 sin x (c) (D + 1) ( D - 2 ) y = er 10. Solve (4D2 + 5D + 1) y = x3 for yp (a) Using the power series expansion of the inverse differential operator. (b) Again, using the method of undetermined coefficients. 11. (a) Solve the homogeneous equation completely. y"" + 6y" + 9y' =0 (b) Demonstrate that the solutions to this equation are linearly independent using the Wron- skian determinant. (c) Given y" + 6y" + 9y' = 2e4 + e-32+ 1 Find yp using operator methods (d) Solve for Up again using the method of undetermined coefficients

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