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Solutions to quiz 2 of math 3113, focusing on finding linear homogeneous constant coefficient differential equations, particular solutions, and general solutions of given differential equations.
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i) (10 Points) Let y(x) = 3xex^ + 2. Find a linear homogeneous constant coefficient differential equation whose solution is y(x).
ii) (10 Points) Consider the differential equation
y′′^ − 4 y′^ + 5y = xe^2 x^ cos(x).
Find the appropriate form of a particular solution yp, but do not determine the values of the coefficients.
iii) (5 Points) The roots of the characteristic equation of a constant coefficient homogeneous differential equation are 2, 2 , 0 , 0 , 0 , 3 ± 5 i. Find the general solution of this differential equation.