"M"is the highest exponent of your polynomial, and "S" depends on the solutions to your characteri s and Exponentials and Trigonometry: If the Right Side of your Differential Equation contains Trigono al form of your particular solution is [A x"+ Bx"-1+ C." - 2 + .. + Dx + E]e" cos(t) + x* [Fx" + Gx" -1+ H x" - 2+ .. .. + Dx + E]e" cos(pe) + x* [Fx" + Gx" -1 + Hx" - .
"M"is the highest exponent of your polynomial, and "S" depends on the solutions to your characteri s and Exponentials and Trigonometry: If the Right Side of your Differential Equation contains Trigono al form of your particular solution is [A x"+ Bx"-1+ C." - 2 + .. + Dx + E]e" cos(t) + x* [Fx" + Gx" -1+ H x" - 2+ .. .. + Dx + E]e" cos(pe) + x* [Fx" + Gx" -1 + Hx" - .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
q7
![y, = x° [A xM + BxM -1+ CxM - 2
+ Dx + E
...
Where " M" is the highest exponent of your polynomial, and "S" depends on the solutions to your characteristic equation.
Powers and Exponentials and Trigonometry: If the Right Side of your Differential Equation contains Trigonometry, then the
general form of your particular solution is
+ BxM -1+ CaM – 2 + .. + Dx + E]e* cos(Bx) + x* [F xM + GxM -1+ H xM -2,
+ ... + k + JJea sin(ßx)
Notice how the coefficients in front of the polynomial portions of the solution does not restart at "A". This means that we can have
several "+ C's " to find in order to find a Specific Solution.
Determine which of the following Differential Equations below would use the following general form for its particular solution.
*[A xM + B xM - 1+ C xM - 2
+ Dx + E]eR
%3D
...
Please note that there will be more than 1 correct answer, so chose all that apply.
A
- 7y" + 9y' + y = 7x cos(4x)
B
y" + 8y' =
(742 - 9) е -2х
C 5y" - 7y' + 8y
6x2 + 7x
D
y" + y' - y =(7x + 3) e cos(4x
)
E
10y" + 7y
3 e8*
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94930702-fbcd-4244-b178-ebe011f78567%2F800d0270-5b62-4e7b-a6f3-b4eb5d562c15%2F6ug156f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:y, = x° [A xM + BxM -1+ CxM - 2
+ Dx + E
...
Where " M" is the highest exponent of your polynomial, and "S" depends on the solutions to your characteristic equation.
Powers and Exponentials and Trigonometry: If the Right Side of your Differential Equation contains Trigonometry, then the
general form of your particular solution is
+ BxM -1+ CaM – 2 + .. + Dx + E]e* cos(Bx) + x* [F xM + GxM -1+ H xM -2,
+ ... + k + JJea sin(ßx)
Notice how the coefficients in front of the polynomial portions of the solution does not restart at "A". This means that we can have
several "+ C's " to find in order to find a Specific Solution.
Determine which of the following Differential Equations below would use the following general form for its particular solution.
*[A xM + B xM - 1+ C xM - 2
+ Dx + E]eR
%3D
...
Please note that there will be more than 1 correct answer, so chose all that apply.
A
- 7y" + 9y' + y = 7x cos(4x)
B
y" + 8y' =
(742 - 9) е -2х
C 5y" - 7y' + 8y
6x2 + 7x
D
y" + y' - y =(7x + 3) e cos(4x
)
E
10y" + 7y
3 e8*
%3D
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