Consider the initial value problemd²ydy9.+14y=4e7t2e-8tdt2dtdyy(0) = −3,-(0) = 4dtWrite down the Laplace transform of the left-hand side of the equation given the initial conditionsYour 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 equationYour answer should be a function of s only.Next equate your last two answers and solve for Y. You haveY =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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Answered: Consider the initial value problem d²y…

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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If V=R\power{3}, and W\index{1} is the xy plane and let W\index{2} is yz-plane: W\index{1}={(x,y,0):x,y∈R} W\index{2}={(0,y,z):y,z∈R} then V is not the direct sum of W\index{1} and W\index{2}.
Please write legibly to avoid confusion of final answer
FIND THE LAPLACE TRANSFORM OF EVERY GIVEN EQUATION. SHOW YOUR COMPLETE SOLUTION.BOX YOUR FINAL ANSWER IN SIMPLIFIED FORM.
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What is the amplitude and phase shift of the equation u(t)=0.2cos3t+0.3sin3t? A = A = A=- 13 10 13 10 13 10 13 10 ; 8= -0.98 ; 8=0.98 ; 8=-0.59 ; 8=0.59
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'-4y+3y=3te, y(0) = 3, y'(0) = -3 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.
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4
Show the intermediate steps. Express your answers in standard form (4 decimal places)
Consider the initial value problem d²y dt2 dy 6. +9y=-2e +9e³t dy -4t y(0) = 8, -(0) = −5 dt 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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