Let P be the differential operator defined by P(y) = (D-4D+5) (D²-1) y a) Using Laplace transforms solve: b) Solve: P(4)=4-5t + tetsint where D=&=' - += y(4) 44 (8) + 4y (2) tay'-sy y (3) (0) = 12. P(y) = 4-st, y(0) = 4, y'(0) = 2, y" (0) = 10,

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A: To find out the characteristic equation.

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A: r(t)=cos(-3t) i+sin(-3t) k-10tk

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A: (Note: Please scroll to the last step for the final answer.) Given equation is 2x2y''−xy'+2x+1y=0…

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A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

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A: 11. Given that the series                      x∑m=1∞mamxm-1+∑m=0∞amxm

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A: Since you have asked multiple questions, we will solve the first Question for you. If you want any…

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Q: Q: Use Lagrange's Formula to Prove that :

A: Solution: We know that Lagrange's interpolation formula for unequal intervals is, f x =  x-x1  x-x2…