(a) Do not solve the following differential equations. State the difference between homogeneous second order differential equation and non-homogeneous second order differential equation. i. ii. The auxiliary equation of a second order differential equation, d?y dy +b + cy = 0 dx? dr has 2 real unequal roots, m = -4 and m = 5. Write the general solution for this equation. ii. Write the trial solution of the particular integral for the following equation, d?y dæ? + 2y = 3e" cos(2x) iv. Can y = Csin(3x)+ Dcos(3x) be the trial solution for the following equation. d²y + 9y = 6cos(3x) da? If your answer is no, explain your answer and suggest a new trial solution.
(a) Do not solve the following differential equations. State the difference between homogeneous second order differential equation and non-homogeneous second order differential equation. i. ii. The auxiliary equation of a second order differential equation, d?y dy +b + cy = 0 dx? dr has 2 real unequal roots, m = -4 and m = 5. Write the general solution for this equation. ii. Write the trial solution of the particular integral for the following equation, d?y dæ? + 2y = 3e" cos(2x) iv. Can y = Csin(3x)+ Dcos(3x) be the trial solution for the following equation. d²y + 9y = 6cos(3x) da? If your answer is no, explain your answer and suggest a new trial solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) Do not solve the following differential equations.
State the difference between homogeneous second order differential equation and non-homogeneous second order differential
equation.
i.
ii.
The auxiliary equation of a second order differential equation,
d?y
dy
+b + cy = 0
dx?
dr
has 2 real unequal roots, m = -4 and m = 5. Write the general solution for this equation.
ii.
Write the trial solution of the particular integral for the following equation,
d?y
dæ?
+ 2y = 3e" cos(2x)
iv.
Can y = Csin(3x)+ Dcos(3x) be the trial solution for the following equation.
d²y
+ 9y =
6cos(3x)
da?
If your answer is no, explain your answer and suggest a new trial solution.
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