1. Answer the following questions. d (A) [50%] Consider the non-homogeneous DE p y = F(x) where dx p(r) = r²(r + 2)³ (r²+4) and F(x) = 9+3xe¯2x − 5 sin(2x) + 12 cos(5x) Write the solution of the corresponding homogeneous DE (i.e., y(x)), and (without trying to determine the coefficients) write the general form of the particular solution yp(x). (B) [50%] Find the solution of the IVP 2y"7y+3yte-3t, y(0) = 0, y'(0) = 1. Then, to 4 decimals compute y(3.027). Find the long-time behaviour of the solution.

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A: Detailed graph If you have any questions let me know in the comment box thankyou.

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