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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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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