1.

Find the general solution by the method of undetermined coefficients.(D2 − 2D + 1)y = x2 + 3x + 1.

Answer»

Since the right-hand side is a polynomial of degree 2, the trial solution should be a polynomial of degree 2, say y = Ax2 + Bx + C.

Now plug this into the left-hand side and solve for the coefficients. The answer is 

y = x2 + 7x + 13 + C1ex + C2xex.



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