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1 1 Almost done! You know Z(y) = -2(+3)+³ (572)· Laplace transform of each term on the right side of this equation. 1 L-¹₁ ( - ² ( + + + ₁)) = [ -2 s +3 L (3 (5 1 s+2 To find y(t), find the inverse

1 1 Almost done! You know Z(y) = -2(+3)+³ (572)· Laplace transform of each term on the right side of this equation. 1 L-¹₁ ( - ² ( + + + ₁)) = [ -2 s +3 L (3 (5 1 s+2 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 5

Please help with the part 4

In this exercise you will use Laplace transforms to solve the differential equation y"+5y'+6y= 0, y(0) = 1, y'(0) = 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') = = L(5y') = = L(6y) L(0) = s²L(y) — 5(sL(y) - 1) 6L (y) L(y) = 0 - S Great! You now have the equation s²L(y) — s + 5sL(y) − 5 +6L(y) = 0. - Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. s+ 5 (s+2) (s+3) Nice! You have shown that L(y) the right side of this equation. 2 3 L(y) = − (573) + (5+2) Almost done! You know L(y) -2 1 1 2 ( 5 + 3) + ³ ( 5 7² 2₂). s s+2 Laplace transform of each term on the right side of this equation. 1 2-¹ ( - 2 ( 5 + 3 ) ) = L s s+5 (s+3)(s+2) 1 [~¹(³ ( ¸ + 2)) = L 3 ▼ Part 2 of 5 Part 3 of 5 Find the partial fraction decomposition of Part 4 of 5 To find y(t), find the inverse
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation y"+5y'+6y= 0, y(0) = 1, y'(0) = 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') = = L(5y') = = L(6y) L(0) = s²L(y) — 5(sL(y) - 1) 6L (y) L(y) = 0 - S Great! You now have the equation s²L(y) — s + 5sL(y) − 5 +6L(y) = 0. - Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. s+ 5 (s+2) (s+3) Nice! You have shown that L(y) the right side of this equation. 2 3 L(y) = − (573) + (5+2) Almost done! You know L(y) -2 1 1 2 ( 5 + 3) + ³ ( 5 7² 2₂). s s+2 Laplace transform of each term on the right side of this equation. 1 2-¹ ( - 2 ( 5 + 3 ) ) = L s s+5 (s+3)(s+2) 1 [~¹(³ ( ¸ + 2)) = L 3 ▼ Part 2 of 5 Part 3 of 5 Find the partial fraction decomposition of Part 4 of 5 To find y(t), find the inverse
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