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7 1 1 Almost done! You know I (y) = ( ) + −1² ( , + 2) 2 2 transform of each term on the right side of this equation. L-1 7 GC)) = 2 1 1 +(-(+)) - 2 s+2 L -1 To find y(t), find the inverse Laplace

7 1 1 Almost done! You know I (y) = ( ) + −1² ( , + 2) 2 2 transform of each term on the right side of this equation. L-1 7 GC)) = 2 1 1 +(-(+)) - 2 s+2 L -1 To find y(t), find the inverse Laplace

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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Homework 9: Question 1

Please help with the part 4

In this exercise you will use Laplace transforms to solve the differential equation y'+2y = 7, y(0) = 3. Find the Laplace transform of each term in the equation. Your answer(s) may contain L(y). Incorporate any initial conditions if necessary. L(y') L(2y) L(7) = = = L(y): L(y) You got it! You now have the equation 7 S SL(y) - 3 2L (y) 7 S sL(y) — 3+2L(y) Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. L Nice! You have shown that L(y) side of this equation. = (7+3s) (s(s+2)) 7 1 = 2s 2(s+2) 7 L -1 - ((:)) - 1 Almost done! You know [(y) 77 ( ² ) + - 1²/ ( 0 ² 2 ) 2 2 transform of each term on the right side of this equation. 1 1 +²^(-(-₂)). 2 s+2 ▼ Part 1 of 5 7+ 3s s(s+2) = ▼ Part 2 of 5 Part 3 of 5 Find the partial fraction decomposition of the right Part 4 of 5 To find y(t), find the inverse Laplace
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation y'+2y = 7, y(0) = 3. Find the Laplace transform of each term in the equation. Your answer(s) may contain L(y). Incorporate any initial conditions if necessary. L(y') L(2y) L(7) = = = L(y): L(y) You got it! You now have the equation 7 S SL(y) - 3 2L (y) 7 S sL(y) — 3+2L(y) Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. L Nice! You have shown that L(y) side of this equation. = (7+3s) (s(s+2)) 7 1 = 2s 2(s+2) 7 L -1 - ((:)) - 1 Almost done! You know [(y) 77 ( ² ) + - 1²/ ( 0 ² 2 ) 2 2 transform of each term on the right side of this equation. 1 1 +²^(-(-₂)). 2 s+2 ▼ Part 1 of 5 7+ 3s s(s+2) = ▼ Part 2 of 5 Part 3 of 5 Find the partial fraction decomposition of the right Part 4 of 5 To find y(t), find the inverse Laplace
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