MATH 3321 Exam 2| Questions & Verified Answers | 2026/2027 Updated | University of Houston -PDF

MATH 3321 Exam 2| Questions & Verified Answers | 2026/2027 Updated |
University of Houston -PDF
wait=-3278607, due=1698555540, due2=0 Question number 1.




Your answer was C. Correct.


Give the form of a particular solution of y′′ − 6y′ + 8y = −3e2x − 5xe−4x + 3x.

A z = Axe2x + (Bx + C)e−4x + D

B z = Ae2x + (Bx2 + Cx)e−4x + Dx + E

C z = Axe2x + (Bx + C)e−4x + Dx + E


D z = Axe2x + (Bx2 + Cx)e−4x + Dx + E

E z = Ae2x + (Bx + C)e−4x + Dx

F None of the above.




Question number 2.



Your answer was D. Wrong.


The linear, homogeneous differential equation of least order that has
y = 5e4x − 4 cos(3x) + 3 sin(3x) + 5 as a solution is:


A y(4) + 4y′′′ − 9y′′ + 36y′ = 0

B y(5) − 4y(4) + 9y′′′ − 36y′′ = 0

C y′′′ − 4y′′ + 9y′ − 12y = 0
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, D y(4) − 4y′′′ + 3y′′ − 12y′ = 0


E y(4) − 4y′′′ + 9y′′ − 36y′ = 0

F None of the above.




Question number 3.




Your answer was D. Correct.


Give the form of a particular solution of y′′′ + 4y′′ + 9y′ + 36y = −3xe−2x + 4 cos(3x) − 5.

(Hint: e−4x is a solution of the reduced equation.)

A z = (Ax + B)e−2x + Cx cos(3x) + Dx sin(3x) + Ex


B z = Ax2e−2x + Bx cos(3x) + Cx sin(3x) + Dx + E

C z = (Ax + B)e−2x + C cos(3x) + D sin(3x) + Ex

D z = (Ax + B)e−2x + Cx cos(3x) + Dx sin(3x) + E


E z = Axe−2x + Bx cos(3x) + Cx sin(3x) + D

F None of the above.




Question number 4.




Your answer was D. Correct.



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