Solve System of Linear differential equations using Laplace transform: Provide all steps First order system of differential equations : Here you apply transform of Derivatives, but not derivative of transform L {y'(t)} = sF(s)- y(0) Problem 4. a) given: x(0) = 0; dx = x + y dt Sheet dy = 3x dt y (0) = 1 on attatched

Solve System of Linear differential equations using Laplace transform: Provide all steps First order system of differential equations : Here you apply transform of Derivatives, but not derivative of transform L {y'(t)} = sF(s)- y(0) Problem 4. a) given: x(0) = 0; dx = x + y dt Sheet dy = 3x dt y (0) = 1 on attatched

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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Question

Answer 4b only Solve System of Linear differential equations using Laplace transform: Provide all steps First order system of differential equations : Here you apply transform of Derivatives , but not derivative of transform ? {y’(t) } = sF(s) – y(0)

Solve System of Linear differential equations using Laplace transform: Provide all steps
First order system of differential equations :
Here you apply transform of Derivatives, but not derivative of transform
L {y'(t)} = sF(s)- y(0)
Problem 4. a)
given: x(0) = 0;
Sheet
dx = x + y
dt
dy = 3x
dt
- on a++atched
y (0) = 1
b) dx + 2x-3dy = 1
dt
dt
dt
dx-x+dy - 2y = et
dx
given: x(0) = 0; y(0) = 0

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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Step 1: Given information:

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Step 2: Applying Laplace transform:

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Step 3: To find Y(s) :

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Step 4: To find X(s) :

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Step 5: Simplify X(s) and Y(s) :

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Step 6: Applying inverse Laplace transform to find x(t) :

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Step 7: Applying inverse Laplace transform to find y(t) :

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