one question about Laplare transform and ODES involving impulse functions: Such as: y"+y= u(t)+38(t−3π/2) - U₂ ( (1); y(0) = 0, y'(0) = 0

Q: Use the Laplace Transform to solve the initial value problem 0St<2T y" + y = ;y(0) = 0, y' (0) = 0.…

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Q: Solve the following IVP by the Laplace transform. y(t) = = y" - 6y + 5y = 174 cos(2t), y(0) = 19.2,…

A: Given IVP y''-6y'+5y=174cos(2t), y(0)=19.2, y'(0)=37.2

Q: Q5/Solve the following ODE using Laplace transform y" - 2y' - 3y = e-2x, y(0) = 2, y'(0) = -1

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Q: Question 3 a) Solve the initial value problem by using the Laplace transform. y" - 5y'+6y = 4sin 3t,…

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Q: Q3) Solve the following initial value problems by Laplace transform. (Show all details): A. y' +4y 0…

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Q: Q5/Solve the following ODE using Laplace transform y" - 2y' - 3y = e-2x, y(0) = 2, y'(0) = -1

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Q: y" - 5y' +6y=et; y(0) = 0; y'(0) = 2

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Q: Use Laplace Transform to solve the initial value problem y' - 2y +2y=cos t y(0) = 0; y'(0)=1 %3D

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Q: 7. Using Lyapunov functions, show that the origin is unstable for the ODE i = -x3 ÿ = -y3

A: The solution is given below

Q: Solve the given initial-value problem using the Laplace transform: -{- = x(0) = 5. x' + 3x if 0<t<4…

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Q: Q5/Solve the following ODE using Laplace transform y" - 2y' - 3y = e-2x, y(0) = 2, y'(0) = -1

A: We will use Laplace transformation table to find Y(s) and then use inverse Laplace transformation…

Q: The general solution of the initial value problem given below is the "Laplace Transform". find using

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Use the Laplace transform to solve the given initial value problem. y"-8y'-84y=0; y(0)=7, y'(0)= 18…

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Q: y" - 5y + 6y = 6(u₂ (t)-us(t)) y(0) = y'(0) = 0

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Q: y" + 3y - 4y = 6e²t-3, y(1.5) = 4, y'(1.5) = 5

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Q: f(t) = 0≤t≤1 1≤t≤2 1 t²-3 t>2

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The Laplace…

Q: y" + y = -2 sin t + 10 8(t – 7), y(0) = 0, y'(0) = 1.

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Q: Find the solution to the ODE below using Laplace Transform: y' +y = e-3t y(0) = 0

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Q: . Use the Laplace Transform Table (LTT) to find F(s) = L{f(t)}(s) if f(t)=t¹+t²e + sin²t - e" sin…

A: Consider the function ft=t4+t2e-t+sin2t-e3tsin3 t. To determine Laplace transform of ft. Laplace…

Q: a"(t) + 16x(t) = 5 sin t, a'(0) = x(0) = 0 %3D

A: First we have to take Laplace transform of the given equation.

Q: 4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) =…

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Q: y" +16y= cos(41) 7. Solve the initial value problem (0) =1 (0)=1 using the Laplace transform. No…

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Q: y" - 5y' +6y=et; y(0) = 0, y'(0) = 2

A: The given initial value problem is .Use the Laplace transform to solve the initial value problem.Use…

Q: Use Laplace transform to solve the initial value problem y"+y=d(tn), y(0)=0 and y'(0) = 0

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

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Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

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Q: Using Laplace transform, sole cỳ"+y= cos x, where y (0) = 0 = y'(0)

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Q: Use Laplace transform to solve the initial value problem x" - 9x = e;x(0) = 1, x'(0) = –1

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Q: Solve the initial value problem below using the method of Laplace transform w"-2w' +w= 5t + 11, w( -…

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