3 Consider the result (1.d) above. We will use it to calculate the solution for the ODE ƒ"(t) + ƒ' (t) + f(t) = e(t-1)e-t as follows. (i) Write the expression in (1.d) in terms of L[f[t]](s) assuming the boundary/initial conditions f'(0) = 0 and f(0) = 0 (ii) Equate it to 0, and solve it for L[f(t)](s). (iii) Calculate the Inverse Laplace transform of the resulting expression to find the solution f(t) to the differential equation.
3 Consider the result (1.d) above. We will use it to calculate the solution for the ODE ƒ"(t) + ƒ' (t) + f(t) = e(t-1)e-t as follows. (i) Write the expression in (1.d) in terms of L[f[t]](s) assuming the boundary/initial conditions f'(0) = 0 and f(0) = 0 (ii) Equate it to 0, and solve it for L[f(t)](s). (iii) Calculate the Inverse Laplace transform of the resulting expression to find the solution f(t) to the differential equation.
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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![3 Consider the result (1.d) above. We will use it to calculate the solution
for the ODE
f"(t) + f'(t) + f(t) = e(t-1)e-t
as follows.
(i) Write the expression in (1.d) in terms of L[f[t]](s) assuming the
boundary/initial conditions f'(0) = 0 and f(0) = 0
(ii) Equate it to 0, and solve it for L[f(t)](s).
(iii) Calculate the Inverse Laplace transform of the resulting expression
to find the solution f(t) to the differential equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37ebe49-731c-47f9-a49b-3a5f656faaa2%2Fa3595ecb-b305-4f3e-9afe-46ed620dc913%2Fy3u9eb_processed.png&w=3840&q=75)
Transcribed Image Text:3 Consider the result (1.d) above. We will use it to calculate the solution
for the ODE
f"(t) + f'(t) + f(t) = e(t-1)e-t
as follows.
(i) Write the expression in (1.d) in terms of L[f[t]](s) assuming the
boundary/initial conditions f'(0) = 0 and f(0) = 0
(ii) Equate it to 0, and solve it for L[f(t)](s).
(iii) Calculate the Inverse Laplace transform of the resulting expression
to find the solution f(t) to the differential equation.
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