1. (25 points) Solve the following Initial Value Problem using the Laplace Transform: y" + 5y' + 6y = e^{2t}, y(0) = 1, y'(0) = 0
Added by Mary A.
Close
Step 1
The Laplace Transform of y'' is s^2Y(s) - sy(0) - y'(0), where Y(s) is the Laplace Transform of y(t). The Laplace Transform of y' is sY(s) - y(0). The Laplace Transform of y is Y(s). Using these formulas, we can rewrite the equation as: s^2Y(s) - sy(0) - y'(0) Show more…
Show all steps
Your feedback will help us improve your experience
Kritika Mishra and 85 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Solve the following initial value problems by Laplace transform. 8. y'' + 3y' + 2y = 0, y(0) = 1, y'(0) = 0. 9. y'' - 2y' + 2y = 0, y(0) = 0, y'(0) = 1. 10. y'' + 2y' + 5y = 0, y(0) = 2, y'(0) = -1.
Madhur L.
Use the Laplace transform to solve the given initial value problem y' = dy/dt. y'' - y' - 20y = 0, y(0) = 1, y'(0) = -1 Y(s) = y(t) =
Scott S.
(25 points) Use the Laplace transform to solve the following initial value problem: y'' - 4y' + 8y = 0 y(0) = 0, y'(0) = 2 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation. Now solve for Y(s). By completing the square in the denominator and inverting the transform, find y(t).
Adi S.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD