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Suppose the equation y" + p(t)y' + q(t)y= f(t) is non- homogenous, has a particular solution y,(t) = sin(t), and that the solution of the complementary equation is Yc(t) = cit + C2e¯. Which of the following is a solution of the following IVP? y" + p(t)y' + q(t)y = f(t), y(0) = 0, y'(0) = 0 O y = sin(t) +1 O y = sin(t) – t O y = t+e-t + sin(t) O y = t+et +t sin(t) O y = cos(t) – 1 O y = 1 – e-t + cos(t) O y = cos(t)+t

Suppose the equation y" + p(t)y' + q(t)y= f(t) is non- homogenous, has a particular solution y,(t) = sin(t), and that the solution of the complementary equation is Yc(t) = cit + C2e¯. Which of the following is a solution of the following IVP? y" + p(t)y' + q(t)y = f(t), y(0) = 0, y'(0) = 0 O y = sin(t) +1 O y = sin(t) – t O y = t+e-t + sin(t) O y = t+et +t sin(t) O y = cos(t) – 1 O y = 1 – e-t + cos(t) O y = cos(t)+t

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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Suppose the equation y" + p(t)y' +q(t)y = f(t) is non- homogenous, has a particular solution yp(t) = sin(t), and that the solution of the complementary equation is Ye(t) = cit + C2e¯t. Which of the following is a solution of the following IVP? y" + p(t)y' + q(t)y = f(t), y(0) = 0, y'(0) = 0 O y = sin(t) +1 O y = sin(t) – t O y = t+et + sin(t) O y =t+et +t sin(t) O y = cos(t) – 1 O y = 1 – e-t + cos(t) O y = cos(t) +t
Transcribed Image Text:Suppose the equation y" + p(t)y' +q(t)y = f(t) is non- homogenous, has a particular solution yp(t) = sin(t), and that the solution of the complementary equation is Ye(t) = cit + C2e¯t. Which of the following is a solution of the following IVP? y" + p(t)y' + q(t)y = f(t), y(0) = 0, y'(0) = 0 O y = sin(t) +1 O y = sin(t) – t O y = t+et + sin(t) O y =t+et +t sin(t) O y = cos(t) – 1 O y = 1 – e-t + cos(t) O y = cos(t) +t
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Step 1 Given

We have to find solution of the IVP y''+p(t)y'+q(t)y=f(t)  , y(0)=0, y'(0)=0 .

Where the equation y''+p(t)y'+q(t)y=f(t) is non-homogeneous, has a particular solution yp(t)=sint and that the solution of the complementary equation is yc(t)=c1t+c2e-t.

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