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7.) (DS +403) = 7 %3D m5 + 4m3 = O

7.) (DS +403) = 7 %3D m5 + 4m3 = O

Advanced Engineering Mathematics
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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7.) (DS +403) = 7 %3D 15+ 4m3 %3D
Transcribed Image Text:7.) (DS +403) = 7 %3D 15+ 4m3 %3D
Particular Solution by Inspection It is frequently easy to obtain a particular solution of a non-homogeneous equation bo(x)- d" y d"-'y dy + b,(x)y = R(x) dx + b1 (x)- +...+ bn-1(x) dxn drn-1 by inspection if R(x) is a constant. Say that R(x) = Ro and if b, # 0, then Ro Yp = bn is a solution of d"y bo(x); d"-'y + b1 (x)- + bn-1(x); dy + b, (x)y = Ro- %3D drn-1 dx Suppose b, = 0 and let Dky the lowest ordered derivative, then Roxk Yp k!bn-k
Transcribed Image Text:Particular Solution by Inspection It is frequently easy to obtain a particular solution of a non-homogeneous equation bo(x)- d" y d"-'y dy + b,(x)y = R(x) dx + b1 (x)- +...+ bn-1(x) dxn drn-1 by inspection if R(x) is a constant. Say that R(x) = Ro and if b, # 0, then Ro Yp = bn is a solution of d"y bo(x); d"-'y + b1 (x)- + bn-1(x); dy + b, (x)y = Ro- %3D drn-1 dx Suppose b, = 0 and let Dky the lowest ordered derivative, then Roxk Yp k!bn-k
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