Using the method of undetermined coefficients, find the particular solution of the following initial value problem: (a). y" + 4y' + 4y = 2te 4, 3(0) = 1, y (0) = –3 %3D %3D General Solutions: 3(t) = a ezp( exp(-2t) + exp( Applying initial conditions Particular Solutions: exp( t exp (b). y" - y – y = 0, 3(0) = 0, y'(0) = 3, y"(0) = 2 General Solutions: y(t) =Ci cos( D+ a sin( te ezp Applying initial conditions a Particular Solutions: y(t) + cos sin( ezp

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Using the method of undetermined coefficients, find the particular solution of the following
initial value problem:
(a). y" + 4y' + 4y = 2te ", y(0) = 1, y(0) = -3
General Solutions: y(t)
=a erp(
exp(-2t) + 4 exp(
Applying initial conditions c =
)-t exp(
)+ exp(
Particular Solutions:
y =
exp(
(b). y" - y – y = 0, y(0) = 0, y'(0) = 3, y" (0) = 2
%3D
General Solutions: y(t) =Ci cos(
)+ a sin
)+a erp
Applying initial conditions c
Particular Solutions: y(t)
cos(
sin(
ezp
Transcribed Image Text:Using the method of undetermined coefficients, find the particular solution of the following initial value problem: (a). y" + 4y' + 4y = 2te ", y(0) = 1, y(0) = -3 General Solutions: y(t) =a erp( exp(-2t) + 4 exp( Applying initial conditions c = )-t exp( )+ exp( Particular Solutions: y = exp( (b). y" - y – y = 0, y(0) = 0, y'(0) = 3, y" (0) = 2 %3D General Solutions: y(t) =Ci cos( )+ a sin )+a erp Applying initial conditions c Particular Solutions: y(t) cos( sin( ezp
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