Solve the given initial value problem using the method of Laplace y" +3y' +2y tu(t- 2); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. (e2 (2t- 3)-4 et+2+3e4) u(t- 2) + 4(et-1)) y(t) = 4e 2t

Q: Q 5(b) Find the inverse Laplace transforms of the following: 3 (i) (s+1)6 1 (ii) s2-2s+5

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Q: 2. (a) Use the method of Laplace transforms to find the solution y(t) of the initial value problem…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Determine £-'{F}. 2 4s + 59s + 195 F(s) = (s + 6) (s + 3) Click here to view the table of Laplace…

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Q: Solve using laplace transforms: - 4y + 4y = 1³e². y(0) = 0, z/(0) = 0

A: y''-4y'+4y=t3e2t, y(0)=y'(0)=0

Q: Solve the initial value problem below using the method of Laplace transforms. 2. y" + 16y = 48t -…

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Q: (iii) Find Laplace transform of the following using the properties of the transform: te-3t (iv)…

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Q: 3 Solve the following equations by Laplace transforms. dx (а) + 3x = e-2t given that x =2 when t = 0…

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Q: Determine the Laplace transforms of 3, 0 12

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Q: Example: Sketch the direction field for the equation y' = y – t over the square -2 < t, y < 2, then…

A: The direction field is a graph of small line segments passing through various points whose slope is…

Q: 25. Find the general solution of the equation dy = 2y + 2e-. dt (This equation is linear, but please…

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Q: 5s F(s) %3D (s + 7) (s? + 4) 35 35 10 -7t Answer: f(t) G, cos2t + sin2t) 53 %3D 53 33

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Q: Solve the initial value problem below using the method of Laplace transforms. ty" - 2ty' + 2y = 8,…

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Q: * + 5x + 6x = 5sin (2t)

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Q: 2. Y(s) = J(2s – 3)5 %3D

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Q: find the Laplace transform of t²cos(wt)

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Q: Use the formula £{t" f(t)} (s) = ( – 1)" – (L{f}(s)) to help determine the following the…

A: We will use formula for derivative of u/v and given formula to solve as follows

Q: 3s Find the Inverse Laplace of s2+4

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Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s2-12s-8] L-1 1)…

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Q: Find Fourierexpansion of the Punction fcx) = x2 XE [-T, TT] then deduce thetn = | 2' (572 (7)2t. (2)…

A: Since you have asked multiple questions, we will solve the first Question for you. If you want any…

Q: √x³+9y³ 5x +COS (+)

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Q: Find the Laplace transform of f(t), where ƒ(t) is f(t)=4e³ sint cost and f(t)=r’sinh2t .

A: We know that  Leat sin(bt) = b(s-a)2+b2. Now  Lf(t)=L4 e3t sint cost= 2 L e3t 2sint cost= 2 L{e3t…

Q: 2. Find the Laplace and Inverse Laplace transforms of the followings: (a) cosh(t)sin(2rt): Hint(cosh…

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Q: Determine the constants a, p, yo and y'o so that 3S +3 Y(s) = (s + 2)² is the Laplace transform of…

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Q: Plot a number of isoclines and construct a direction field for the equation dy dy y = x- dx dx If…

A: Given the differential equation y=xdydx+dydx2.…

Q: How did they get Y(s)? I tried, but I don't get how to convert the y' notation.

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Q: 2. (a) Find the Laplace transform of the function f(t)=4e¹-4te-2 +21²e-3t 0 (b) Find the Laplace…

A: Part a and b asked and answered.

Q: (D² + 2D- 3)y = sin 2x; y(0) = y'(0) = 0 (Use The Laplace Transform)

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