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Consider the initial value problem d²y dy 9. +14y=4e7t2e-8t dt2 dt dy y(0) = −3, -(0) = 4 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution Y. Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You have Y = Your answer should be a function of s only. Finally take the inverse laplace transform of your third answer to obtain the solution of the given initial value problem. y(t) Your answer should be a function of t.

Consider the initial value problem d²y dy 9. +14y=4e7t2e-8t dt2 dt dy y(0) = −3, -(0) = 4 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution Y. Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You have Y = Your answer should be a function of s only. Finally take the inverse laplace transform of your third answer to obtain the solution of the given initial value problem. y(t) Your answer should be a function of 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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Consider the initial value problem d²y dy 9. +14y=4e7t2e-8t dt2 dt dy y(0) = −3, -(0) = 4 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution Y. Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You have Y = Your answer should be a function of s only. Finally take the inverse laplace transform of your third answer to obtain the solution of the given initial value problem. y(t) Your answer should be a function of t.
Transcribed Image Text:Consider the initial value problem d²y dy 9. +14y=4e7t2e-8t dt2 dt dy y(0) = −3, -(0) = 4 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution Y. Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You have Y = Your answer should be a function of s only. Finally take the inverse laplace transform of your third answer to obtain the solution of the given initial value problem. y(t) Your answer should be a function of t.
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