Please do d and f 0,and find the Laplace tranform X (s).t<6,t≥ 6,6. Solve the following initial value problems using Laplaca) a' + 5x = H(t-2), x(0) = 1.b) x' + x = sin 2t, x(0) = 0.c) x" - x² - 6x=0,d) x" - 2x² + 2x = 0,e) x" - 2x' + 2x = e-t,f) x" - x' =0, x(0) = 1, x'(0) = 0.g) x" +0.4x' + 2x = 1 - H(t-5), x(0)=0, x'(Ch) r" +9x = sin 3t, x(0) = 0, x'(0) = 0.i) x"-2x = 1, x(0) = 1, x'(0) = 0.j) x' = 2x + H(t-1),x(0) = 0.7. Sketch the function f(t) = 2H(t - 3) - 2H(t-=transform.Tx(0) = 2, x'(0) = -1x(0) = 0, '(0) = 1.x(0) = 0, r' (0) = 1.8. Find the Laplace transform of f(t) = t²H(t-3).9. Invert F(s) =

Answered: Image /qna-images/answer/43d60094-b1ba-42a5-80e8-1c22f8e8ede0.jpg

Answered: d) x" - 2x² + 2x=0, e) x" - 2x' + 2x =…

d) x" - 2x² + 2x=0, e) x" - 2x' + 2x = e-t, x(0)=0, x'(0) = 1. x(0) = 0, r' (0) = 1. f) x" - x' = 0, x(0) = 1, x'(0) = 0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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Question

Please do d and f

0,
and find the Laplace tranform X (s).
t<6,
t≥ 6,
6. Solve the following initial value problems using Laplac
a) a' + 5x = H(t-2), x(0) = 1.
b) x' + x = sin 2t, x(0) = 0.
c) x" - x² - 6x=0,
d) x" - 2x² + 2x = 0,
e) x" - 2x' + 2x = e-t,
f) x" - x' =0, x(0) = 1, x'(0) = 0.
g) x" +0.4x' + 2x = 1 - H(t-5), x(0)=0, x'(C
h) r" +9x = sin 3t, x(0) = 0, x'(0) = 0.
i) x"-2x = 1, x(0) = 1, x'(0) = 0.
j) x' = 2x + H(t-1),
x(0) = 0.
7. Sketch the function f(t) = 2H(t - 3) - 2H(t-=
transform.
T
x(0) = 2, x'(0) = -1
x(0) = 0, '(0) = 1.
x(0) = 0, r' (0) = 1.
8. Find the Laplace transform of f(t) = t²H(t-3).
9. Invert F(s) =

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