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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 53E
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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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