Transform the differential equation -2y + 4y = cos(at) y(0)=-6 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y. (not Y(s)). Therefore Y =

Q: The signal x() exp(-at)u(t) is passed as the input to a system with impulse response…

A: We have given a signal ..with the help of the Fourier transform we find energy ..the procedure is…

Q: Use the Laplace transform to solve the given initial-value problem. y' - y = 2 cos(9t), y(0) = 0…

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Q: y = sin(x) + 2 y = 2 sin(x) y = (1/2) sin(x) y = – sin(x) y = 3 sin(x) – 5.  Explain the changes…

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Q: D. Solve the differential equation using Loaplace transform of y" + y = 6sin 2t ; when y(0) = 3 and…

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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: Given the differential equation y'' - 3y' - 4y = 0, y(0) = 2, y'(0) = -1 Apply the Laplace Transform…

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Q: y" - 8y' + 16y = e5t; y(0) = 1, y'(0) = 8

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Q: using Laplace transform, solve the equation below. y'' -2y' + 2y = cos (t)         y(0) = 1,  y'(0)…

A: To find the solution of differential equation we use the properties of Laplace transform of…

Q: Solve the equation subject to the given conditions. d'y dy dx² dx 6y=4, y(0)=3, y'(0)=2

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Q: 1. Linearize each function about the indicated xo and express your answer in the form y a yo + m (x…

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Q: can the differential equation be solved using the Laplace Transform? A=3 please quickly

A: To solve the given initial value problem using Laplace transformation: x''t−3x't+2xt=3e2t,…

Q: Q1) Solve the following equation with Laplace Transform Method (Inverse Laplace the equation to find…

A: Given differential equation is y''−3y'−4y=3e2x and y0=1 and y'0=0 Take Laplace transform of…

Q: Let Y(s) be the Laplace transform of y(t). Find the equation satisfied by Y(s) when solving the…

A: Introduction: The Laplace transformation is a very important tool in solving an initial value…

Q: Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an…

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Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: y" + 5y' + 4y = e³t ;y(0) = 0, y'(0) = 1

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Q: Using Laplace transform, solve y"+25y=t, y(0)=1 and y'(0)=0.04

A: Given that, y''+25y=t, y(0)=1, y'(0)=0.04 The laplace transform for, Ly''=s2y(s)-sy(0)-y'(0)Lt=1s2…

Q: Write down the auxiliary (characteristic) equation and then find a general solution of the given…

A: Hiven differential equations are (a)  and (b) .We need to find the auxiliary equation and then…

Q: Using Laplace transform, find the solution to the differential equation y" + 4y' + 3y = 8te' + 6e²…

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Q: dy = e*; y(0) = 2, using the method by Laplace transform. Solve Ans. et +1

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Q: Solve the nonhomogeneous differential equations y" + 25y = 18 cos(4x) + 18 sin(4.x). Do not use the…

A: Solution of given differential equation is the sum of complementary and particular solution

Q: Q3:- (4) Solve the following differential equation: y³ −3y¹ +3y″ − y" = x² 1 (B) Find the inverse…

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Q: 1) Solve U = Uz + U, u(1,t = 0) = sin(e¯² ) cos z, COS T, %3D %3D

A: Given,             and

Q: Transform the differential equation -3y + 4y - 4y = sin(at) y(0) = Therefore Y = = -4 y = -4 into an…

A: Given -3y''+4y'-4y=sina t Also given y0=-4,   y'0=-4   To transform the equation into an algebraic…

Q: In a well-written paragraph, explain the method of solving a differential equation using Laplace…

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Q: dy 3 If , x° + 2xy - y' = 11 find (2, 3) dx by Implicit Differentiation. (so take the derivative and…

A: We have to find the value of dydx(2,3).

Q: Transform

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Q: Consider the following: 7 cos(x) sin(y) = 8 (a) Differentiate with respect to x (y is a function of…

A: Given: 7cosxsiny=8 We know that product rule of differentiation is defined as  fxgx'=f'xgx+fxg'(x)

Q: 5.(i) Solve the differential equation (Dª – 1)y = 2 cos² x (ii) Find the Laplace transform of L[e 2t…

A: Part(i):   The general solutions of the nonhomogeneous equation is follows as y = yc + yp   The…