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Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the differential equation y" + 3y' + 5y = 0, y(0) = - 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = To solve an initial value problem using the Laplace transform takes three steps. 1. Take the Laplace transform of both sides of your ODE. This transforms your ODE into an ALGEBRAIC equation! 2. Solve the resulting algebraic equation for Y(s) 3. Take the inverse Laplace transform. Your result is the solution, y(t).

Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the differential equation y" + 3y' + 5y = 0, y(0) = - 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = To solve an initial value problem using the Laplace transform takes three steps. 1. Take the Laplace transform of both sides of your ODE. This transforms your ODE into an ALGEBRAIC equation! 2. Solve the resulting algebraic equation for Y(s) 3. Take the inverse Laplace transform. Your result is the solution, y(t).

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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Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the differential equation y" + 3y' + 5y = 0, y(0) = - 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = To solve an initial value problem using the Laplace transform takes three steps. 1. Take the Laplace transform of both sides of your ODE. This transforms your ODE into an ALGEBRAIC equation! 2. Solve the resulting algebraic equation for Y(s) 3. Take the inverse Laplace transform. Your result is the solution, y(t).
Transcribed Image Text:Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the differential equation y" + 3y' + 5y = 0, y(0) = - 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = To solve an initial value problem using the Laplace transform takes three steps. 1. Take the Laplace transform of both sides of your ODE. This transforms your ODE into an ALGEBRAIC equation! 2. Solve the resulting algebraic equation for Y(s) 3. Take the inverse Laplace transform. Your result is the solution, y(t).
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