In Exercises 1-31 use the Laplace transform to solve the initial value problem. 1. $y'' + 3y' + 2y = e^t$, $y(0) = 1$, $y'(0) = -6$
Added by Jamie M.
Close
Step 1
The Laplace transform of the left side of the equation is given by: L{y''} + 3L{y'} + 2L{y} Using the properties of the Laplace transform, we can simplify this expression as follows: s^2Y(s) - sy(0) - y'(0) + 3(sY(s) - y(0)) + 2Y(s) where Y(s) is the Laplace Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 99 other Calculus 1 / AB 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
Adi S.
Use the Laplace transform to solve the given initial-value problem. y'' - 3y' + 2y = δ(t - 1), y(0) = 0, y'(0) = 0 y(t) = (e^{2t} - e^{t-1}) U(t - 1) y(t) = (e^{2t-2} + e^{t-1}) U(t - 1) y(t) = (e^{2t} + e^{t-1}) U(t - 1) y(t) = (e^{2t-2} - e^{t-1}) U(t - 1)
Madhur L.
In Problems, use the Laplace transform to solve the given initial-value problem. $$ y^{\prime \prime}-6 y^{\prime}+13 y=0, \quad y(0)=0, \quad y^{\prime}(0)=-3 $$
The Laplace Transform
Translation Theorems
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD