Use the Laplace transform to solve the following initial value problem y" + 16y=86(t-6) Use step(t-c) for ue(t) y(t)- step(t-6)(1/2-1/2cos(4(1-6))) y(0) 0, '(0)-d

Q: Use the Laplace transform to solve the initial value problem y' +4x²y = -28 -25 (t-1) +S(t-1), y(0)…

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

Q: Find Laplace transform of x(t)=t (cos)^2 (wt)u(-2t). *

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Q: 6) f(t-5) if F(f(e))= sinc (w) v2.7

A: We know the following shift property of the Fourier transformation. Ff(t-t0)=e-iwt0Ff(t) Here,…

Q: Which of the following is the expression to be ob tained when the Laplace transform is applied to…

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Q: 0. Use the method of Laplace transform to solve the initial value problem y' (0) = aa + b3. y" -…

A: The solution is given below

Q: Q4 Solve step Functions in Laplace transform t < 6 x ≥ 0 f(t)= = { = 8+ (-8+ (t-6)²

A: The given problem is to find the Laplace transform of the given unit step function. Use the…

Q: Now let's have you try to use these formulae. Find the inverse laplace transform of y'(t),y''(t),…

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Q: 3. Use Laplace transform to solve the IVP y" + 9y = e', y(0) = 0, y'(0) = 0. %3D %3D

A: Laplace transferom, solve the intial value problem

Q: Compute the derivative (r₁(1) r2(1)) if r₁(t) = (t¹0, 1³, tº) 73 10t r2(t) = (et, e³t, elor) (Use…

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Q: D) y y(0) c) y" + 4y + 3y = 8(t-2), y(0) = 1, y'(0) = -1

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Q: Let L(y(t)} = Y (s) Which of the following can be obtained when Laplace transform applied to the…

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Q: 2. Use the Laplace Transform to solve the following system x'= x-5y, y'=-5x+y, x(0)=1, y(0)=1.

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Q: 6. Use the Laplace transform to solve the following IVP. The table is on the next page. y" + 3y' -…

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Q: I have not yet been taught Laplace Transform by my lecturer, I believe. Isn't there another way…

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Q: Please help me solve using the Laplace Transform y''-7y'+10y =9cos(t)+7sin(t)            y(0) = 5,…

A: solution:Given the differential equationy''-7y'+10y=9 cos t+7 sin t   y0=5, y'0=-4Taking laplace…

Q: 2. Let 2s6 s³3s2 + 4s - 12 Find the inverse Laplace transform, y(s). Y(s):

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Q: 8

A: The equation of the line given is in the form x-2y-1=0, which can be rewritten in the…

Q: Which of the following is the expression to be ob tained when the Laplace transform is applied to…

A: We are given the differential equation :  2y''-3y'-2y=te2t Applying Laplace transform to both the…

Q: 6. Use the Laplace Transform to solve the initial value problem: y' +9y = e-tcos (2t), y(0) = 0

A: Given that the initial value problem y'+9y=e-tcos2t   , y0=0    .

Q: Use the Laplace transform method to solve the IVP: 2. (a) y"-2y'+y=te', y(0) = 0, y'(0) = 0

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: [2.] Solve the IVP yu+ 6y'+9y= e-*cos 2x COS2X t. Fed the Laolace transform

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Q: What is the valuea +b+e for Y()= + problem given by y"+ 7y'+ 6y -e', y(0) = 0, y (0) = 02 which is…

A: Given differential equation is y''+7y'+6y=-e-t, y(0)=0, y'(0)=0.

Q: (a) The Legendre's Equation (1-x)y"-2y+n (n+ 1)y=0 where n is a constant. Express the following…

A: For (3), We are given the Legendre's Equation 1-x2y''-2xy'+n(n+1)y=0 where n is a constant. Now, we…

Q: Q2. For each of the following z-transforms, determine the inverse: (a) Ya(z) = (1 –z-1) (1 – 2z-1)(1…

A: Let X(z) be a  Z-transform then the inverse of  Z-transform is defined by x[n]=Z-1X(z) Now, the…

Q: Q4. Solve three of the following: (4) L-1 2s²6s+5 -6s2 + 11s-6) - (( Laplace Transforms 4s +5 -1)²…

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Q: 2- 8. Express the given function using unit step functions and compute its Laplace transform Attempt…

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