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1 1 17 1 Almost done! You know I(3)=(²6) + +7 (8²3) L(y) 9 9 +3 Laplace transform of each term on the right side of this equation. 1 1 2-¹ (G (₁².)) - -1 9 S- 6 17 1 -((--))-[ 9 +3 = To find y(t), find the inverse

1 1 17 1 Almost done! You know I(3)=(²6) + +7 (8²3) L(y) 9 9 +3 Laplace transform of each term on the right side of this equation. 1 1 2-¹ (G (₁².)) - -1 9 S- 6 17 1 -((--))-[ 9 +3 = To find y(t), find the inverse

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 2

Please help with part 4

In this exercise you will use Laplace transforms to solve the differential equation y'+3y = et, y(0) 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') SL(y) - 2 L(3y) 3L (y) 1 L(et) = (s-6) You got it! You now have the equation 1 sL(y) − 2 + 3L(y) S 6 - L(y): = Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. L(y) = 2. Nice! You have shown that L(y) the right side of this equation. = 17 1 1 1 + 9 s +3 9 s-6 L 1 1 9 (s S- + - 17 1 9 (s+3) 17 1 +(())-[ 9 +3 2s - 11 (s - 6) (s + 3) Part 2 of 5 Laplace transform of each term on the right side of this equation. 1 1 +¹( ( ₁² )) - L-¹ 9 S Part 3 of 5 Find the partial fraction decomposition of 17 1 Almost done! You know [(y) 1 ( 1²6 ) + + + 7 (2+3) To find y(t), find the inverse 9 9 Part 4 of 5
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation y'+3y = et, y(0) 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') SL(y) - 2 L(3y) 3L (y) 1 L(et) = (s-6) You got it! You now have the equation 1 sL(y) − 2 + 3L(y) S 6 - L(y): = Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. L(y) = 2. Nice! You have shown that L(y) the right side of this equation. = 17 1 1 1 + 9 s +3 9 s-6 L 1 1 9 (s S- + - 17 1 9 (s+3) 17 1 +(())-[ 9 +3 2s - 11 (s - 6) (s + 3) Part 2 of 5 Laplace transform of each term on the right side of this equation. 1 1 +¹( ( ₁² )) - L-¹ 9 S Part 3 of 5 Find the partial fraction decomposition of 17 1 Almost done! You know [(y) 1 ( 1²6 ) + + + 7 (2+3) To find y(t), find the inverse 9 9 Part 4 of 5
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