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In this exercise you will use Laplace transforms to solve the differential equation y'+3y=et, y(0) = 2. 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 (est) = (3-6) = L(y) You got it! You now have the equation 1 sL(y) - 2+3L(y) Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. = - S- Part 2 of 6

In this exercise you will use Laplace transforms to solve the differential equation y'+3y=et, y(0) = 2. 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 (est) = (3-6) = L(y) You got it! You now have the equation 1 sL(y) - 2+3L(y) Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. = - S- Part 2 of 6

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 2

In this exercise you will use Laplace transforms to solve the differential equation y+3y=et, y(0) = 2. 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) L(et) = = You got it! You now have the equation 1 1 (s - 6) sL(y) − 2 + 3L(y) L(y): = = S 6 Part 1 of 5 Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. Part 2 of 5
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation y+3y=et, y(0) = 2. 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) L(et) = = You got it! You now have the equation 1 1 (s - 6) sL(y) − 2 + 3L(y) L(y): = = S 6 Part 1 of 5 Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. Part 2 of 5
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