Use Laplace Transform to solve the following initial- value problem: (2) dx + xy 4x y(0) = 0, ỳ(0) = v2 %3D

Q: (3) Solve the initial value problem using Laplace transform. y + 4y sin 3t, y(0) = 5.

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Q: (x' = x- 2y V = 5x – yi x(0) = -1, y(0) = 2. %3D %3D %3D %3D

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Q: Use Laplace transform to solve: du ди -x = 0; u(x,0) = e*, u(0,t) = 0. at %3D %3D ax

A: Solution

Q: Use the Laplace transform to solve the given initial-value problem. y' - 2y = 5(t – 4), y(0) = 0…

A: The solution is given as

Q: f (x) = 5.6 sin (2.6x – 4.2) – 9.1- What is the equation of the midline of the function %3D o y =…

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Q: x* (t) – x(t) = 4 cost with x(0) = 0, x' (0) = 1 %3D y = 2e with y(0) = – 1 y - y = e -* with y(0) =…

A: Take the Laplace transform on both sides of the equation.

Q: f(t) = 2t2 - 5 sin(3t) %3D L{f(t)}

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ? 3x²y = x+y 3x²y = 2x-y…

A: Given the differential equation: x2dy+yx+ydx=0 with y1=1 To find out which function satisfies the…

Q: Using Z-transforms, y(k+1)+y(k) given that y(0) = 2. solve the following difference equation: = 14k

A: Solving the z tranform equation

Q: Solve the IVP using Laplace Transform y" = y + 2y, y(0) = -2, y (0) = 3.

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Q: (6) Solve the Integro-differential equation: +4y +5 y(t) dt = e-t; y(0) = 0 dx (7) Find the Fourier…

A: Given Integro-differential equation is dydx+4y+5∫0xy(t) dt = e-t y(0)=0 The given equation can be…

Q: A dog is walking in a straight line on the road looking for bones. The dog is attracted to the smell…

A: The function x(t) indicates the position of dog with respect to time, t. So, the velocity of dog is…

Q: find dy/dx if x=(t2-2t+1)e3t and y=(t2+4t+4)e3t

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Q: g(x) g'(5) = 2 X 13 1+t2 dt

A: Given query is to find indicated derivative.

Q: 7. Use the Laplace transform to solve the difference equation 3x (t) 4x(t-1) = 1, x(t)=0 for t < 0.…

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Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: ii. f(t)= e*tsinhrt 't sinh at

A: Laplace transform formulae: 1. Ltnf(t)=(-1)ndndsnLf(t) 2. Leatf(t)=Lf(t)s→s-a Given: f(t)=e3ttsinhπt

Q: Find the function y = f(x) whose graph passes through the point (5π/12,3.5)if dy/dx =cos(2x−π/3).

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Q: dy dx (²), y(a)= A. (a) Show that by introducing the new dependent variable v(x) by the relation y =…

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Q: 6- Solve the fractal differential equation 5D" y + 5(2y) = x²

A: The  given   equation  is   Taking  Laplace transform on both sides  of  we get,…

Q: Use the Laplace transform to solve the given initial-value problem. у" + 2y" - у' - 2у %3 sin(3t),…

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Q: what is the phase shift of f(x)=16sin(8x-11)-16?

A: Consider the given function.

Q: Use the Laplace transform to solve the following initial value problem: y''+8y'=0, y(0)=-2,…

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Q: w f(z) = z' +z+ 12 Is an Analytic

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Q: Using the Laplace transform, solve the following initial value problem: y"-4y=6e3t - 3et; y(0) = 1,…

A: Step 1: change into laplace form  Step 2: use the condition that given in question  Step 3: slove…