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Use the Laplace transform to solve the following initial value problem: x' = 12x + 4y, y -8x + e¹t x(0) = 0, y(0) = 0 Let X(s) = L{x(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s):

Use the Laplace transform to solve the following initial value problem: x' = 12x + 4y, y -8x + e¹t x(0) = 0, y(0) = 0 Let X(s) = L{x(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s):

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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Use the Laplace transform to solve the following initial value problem: x = 12x + 4y, y -8x + et X(s) Y(s) = = Let X(s) = L{x(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): = x(t) y(t): = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DES: = x(0) = 0, y(0)=0 =
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: x = 12x + 4y, y -8x + et X(s) Y(s) = = Let X(s) = L{x(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): = x(t) y(t): = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DES: = x(0) = 0, y(0)=0 =
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