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MATH 3113 Quiz 2 Solutions: Differential Equations, Quizzes of Mathematics

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.

Typology: Quizzes

Pre 2010

Uploaded on 08/30/2009

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MATH 3113 Quiz 2 Sep. 26,2008
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
y00 4y0+ 5y=xe2xcos(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±5i. Find the general solution of this differential equation.
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MATH 3113 Quiz 2 Sep. 26, 2008

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.