Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y' denote differentia x'- 3x - 9y = 3 x(0) = 0 3 y(0) = -2 -x+y'- 3y = 0 Click the icon to view information on Laplace transforms. x(t) = y(t) = (Type exact answers in terms of e.)

Q: 5. Show how the origin changes stability as a changes by using the Poincaré Diagram. x - [i :]• 2 a…

A: The stability of fixed points of a system of constant coefficient linear differential equation of…

Q: i). ƒ (t) = ²) ² ii). ƒ (t) =t²sinh (21) (5–31

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Q: Rectangle PQRS is reflected across the x-axis. The image is P'Q'R'S'.Which two further…

A: Given Rectangle PQRS is reflected across x axis then image is P'Q'R'S'

Q: Find sine transform of e-[165]t/t

A: The Fourier sine transform is defined as                                  Fsfx = Fss = ∫0∞fx sinsx…

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

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Q: 5 sinh (3t) +4 cosh (3t)

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Q: 5. Use implicit differentiation to find y'. a) хеУ 3 х — у

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Prove that Between any two rational numbers there exist an irrational number .

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Q: The slope of the tangent line at any point (x, y) on a curve is 25 If the point (9, 3) is on the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.