Q2) Given the differential equation d²x dx + 5. + 4x = 10 u(t) dt dt2 a) Find x(t) for the case that the initial conditions are zero using Laplace transform. b) Find x(t) for the case with initial conditions, x(0) = 0 and x(0) = 1, using Laplace transform.

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A: The differential equation is: -2y'+4y=cosat; y0=-6. We have to transform the given differential…

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Q: Solve the simultaneous ODES (a) (b) y"(t) + y'(t)- 2y(t) = sin t., x'(t) + x(t)- 3y(t) = 0 -

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Q: Q2) Solve the Second Order Deferential Equation By using the following: y (0) = 2, y'(0) = 1 y" +…

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Q: 2s + 7s +1 (s+ 5)(s² +4s+5)

A: To find the partial fraction of the expression 2s+7s+1s+5s2+4s+5, determine the values of A, B and…

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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: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: using Laplace transform. S=10h 'T=coh Ft = ht+by - banjos (8)

A: The given differential equation is:y''-4y'+4y=4cos2t;  y0=2,  y'0=5. We have to solve using Laplace…

Q: y''+9y=10e-t,y(0)=0,y'(0)=0 by laplace transform

A: The objective of this question is to solve the given second order differential equation using…

Q: (c) f(t) = 3tan 4t

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Q: a' +x = 6+ 8(t – 4), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: Solve the IVP y""+y'=e*, y(0) = y'(0) =y" (0) = 0 using Laplace transform.

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

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Q: Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

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Q: I Choose the figure that shows an angle of - radians in standard position. 2 Choose the correct…

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

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

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

Q: 22) Solve using Laplace Transform y" + 2y' +5y = etsint where y(0) = 0, y'(0) = 1

A: Solution to the differential equation by using Laplace transform

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: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

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Q: y''-3y'+10y=e-2t , y(0) =0, y'(0)=1

A: We have to solve given problem:

Q: Solve the initial value problem using Laplace Transform of: y'' - 3y'+10y = e-2t when y(0)=0,…

A: Given initial value problem is y''-3y'+10y=e-2t,y0=0, y'0=1 To find the solution of the equation.

Q: Q1) Solve the Second Order Deferential Equation by using Laplace Transform. y" + 6y' + 8y = 0, y(0)…

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Q: Q6. Solve the partial differential equation by using the Laplace transform: ди du +5=21², with the…

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Q: Answer the following questions and show all of your work. (a) Sketch the following function where…

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Q: solve the equation by Laplace transform. y'' - 3y' + 2y = exp(3t),  y(0) = 1, y'(0) = 0

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Q: Qi Write the order and degree of the given. ODE'S.check either these equations aye nón-linear. Also…

A: Consider the given function. y''+x2y-2y'=sinx As the maximum order of the derivative is 2.  So, the…

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

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