Consider the IVP x" + 3x + 2x = H(t− 1)H(3 – t), x(0) = x' (0) = 0, where H (t) is the Heaviside step function. Find the correct solution, expressed as a convolution, among the options below 0, Sile-t+r. -e-2t+2r] dr, Si le-t+r -e-2t+²T]dt, Ox(t) = f[e¹ + 2e¯²7]H(t − 7)H(7 − t + 1)dr 0, t = [0,3) t€ [1,3] t> 3 x(t) = x(t) = x(t) = 2[e-te-2t], 0 0, t = [0, 3) te [1, 3] t> 3 fedr, ₁³e-2(t-¹)dt, t = [0,3) te [1, 3] t> 3
Consider the IVP x" + 3x + 2x = H(t− 1)H(3 – t), x(0) = x' (0) = 0, where H (t) is the Heaviside step function. Find the correct solution, expressed as a convolution, among the options below 0, Sile-t+r. -e-2t+2r] dr, Si le-t+r -e-2t+²T]dt, Ox(t) = f[e¹ + 2e¯²7]H(t − 7)H(7 − t + 1)dr 0, t = [0,3) t€ [1,3] t> 3 x(t) = x(t) = x(t) = 2[e-te-2t], 0 0, t = [0, 3) te [1, 3] t> 3 fedr, ₁³e-2(t-¹)dt, t = [0,3) te [1, 3] t> 3
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
B1.
![Consider the IVP
x" + 3x + 2x = H(t − 1)H(3 – t),
x (0) = x' (0) = 0,
where H(t) is the Heaviside step function.
Find the correct solution, expressed as a convolution, among the options below
t = [0,3)
t = [1,3]
S₁³ [e-t+r_e-²¹+²+]dT,
е
t>3
· x(t) = fő [e¯¹ + 2e¯²¹]H(t − 7)H(7 − t + 1)dr
t = [0, 3)
t = [1,3]
t> 3
x(t) =
x(t) =
=
x(t) =
=
0,
Si le-t+re-2t+²+ ]dt,
е
0,
{
2[e-te-2t],
0,
fe-(-)]dr,
S₁³e-²(t-¹)dt,
t = [0,3)
te [1,3]
t> 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90327120-96ae-430f-aeb4-7b7c1a589d72%2F6da8451b-5cb4-418c-b0af-dc8fe7439f7b%2Foecebyo_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the IVP
x" + 3x + 2x = H(t − 1)H(3 – t),
x (0) = x' (0) = 0,
where H(t) is the Heaviside step function.
Find the correct solution, expressed as a convolution, among the options below
t = [0,3)
t = [1,3]
S₁³ [e-t+r_e-²¹+²+]dT,
е
t>3
· x(t) = fő [e¯¹ + 2e¯²¹]H(t − 7)H(7 − t + 1)dr
t = [0, 3)
t = [1,3]
t> 3
x(t) =
x(t) =
=
x(t) =
=
0,
Si le-t+re-2t+²+ ]dt,
е
0,
{
2[e-te-2t],
0,
fe-(-)]dr,
S₁³e-²(t-¹)dt,
t = [0,3)
te [1,3]
t> 3
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