Undetermined Coefficeints Method The table is in the picture Solution Steps: 1. Solve for Yc. 2. Set up Yp equation using the table a. Duplication of terms in Yp is eliminated by cancelling out duplicated terms. b. Check Yp against Yc. Duplication of terms is eliminated by multiplying the duplicated term in Yp by x raised to the lowest positive integer which eliminates duplication of terms. 3. Substitute Yp into original DE. Ø(D)Yp = f(x) 4. Solve arbitrary constants A,B,C.. by equating coefficients. 5. Substitute values of constants in Yp 6. Add Yp with Yc to get the General Solution: Y = Yc + Yp Solve the following differential equation: 1.(D3 + D) y = 2x2 + 4sinx
Undetermined Coefficeints Method The table is in the picture Solution Steps: 1. Solve for Yc. 2. Set up Yp equation using the table a. Duplication of terms in Yp is eliminated by cancelling out duplicated terms. b. Check Yp against Yc. Duplication of terms is eliminated by multiplying the duplicated term in Yp by x raised to the lowest positive integer which eliminates duplication of terms. 3. Substitute Yp into original DE. Ø(D)Yp = f(x) 4. Solve arbitrary constants A,B,C.. by equating coefficients. 5. Substitute values of constants in Yp 6. Add Yp with Yc to get the General Solution: Y = Yc + Yp Solve the following differential equation: 1.(D3 + D) y = 2x2 + 4sinx
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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Question
Undetermined Coefficeints Method
The table is in the picture
Solution Steps:
1. Solve for Yc.
2. Set up Yp equation using the table
a. Duplication of terms in Yp is eliminated by cancelling out duplicated terms.
b. Check Yp against Yc. Duplication of terms is eliminated by multiplying the duplicated term in Yp by x raised to the lowest positive integer which eliminates duplication of terms.
3. Substitute Yp into original DE.
Ø(D)Yp = f(x)
4. Solve arbitrary constants A,B,C.. by equating coefficients.
5. Substitute values of constants in Yp
6. Add Yp with Yc to get the General Solution: Y = Yc + Yp
Solve the following
1.(D3 + D) y = 2x2 + 4sinx
Transcribed Image Text:f(x)
α
axn
emx
acosbx
asinbx
General Form:
General Solution:
Yp form
Axn +Bxn-1 +...+Cx +D
A
Aemx
Acosbx + Bsinbx
(D)y = f(x)
Acosbx + Bsinbx
Y = Yc+ Yp
Yp will be based on the f(x) term, using A,B,C... as arbitrary constants which
may be solved by equating coefficients.
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