y"" - 4y" + 5y' - 2y = 7t-5, y(0) = 0, y'(0) = 0, y'(0) = -2

Q: y" – 7y' + 12y = 4t where y(0) = 1 and y'(0) = 0

A:

Q: t2 sin wt

A: We have the formula  L{tnf(t)}=(-1)ndnFdsn(s), where F(s)= L{f(t)}

Q: y" + y = √2 sen √2t, y(0) = 10, y'(0) = 0

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Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: (cos(t - 27/3 ) t> 2/3 .Find I f(t) if f(t) = t<0

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Q: f(d) = e-2d d4

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Q: Find the Laplace Transform of the function. Show your work. f(x) = sinh(ax)

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Q: dt (te-¹u (t))?

A:

Q: 1. (a) Use the Laplace transform method to solve the IVP: y"+4y=4-4u(t-л): y(0)=0, y'(0) = 0 (b)…

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Q: Use the Laplace transform to solve the initial-value problem x" + 4x = f(t), x(0) = 0, x'(0) = 0,…

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Q: y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: 10. Find the Laplace transform of 10 cos Tt (1 < t < 2)

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Q: Hicit Differentiation yt= 4xy

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Q: L[sin(3t - 4n)]

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Q: Laplace transform of derivatives Find [ (t² 3t + 2)sin3t.

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Q: d²x dx (v) - 2 + 10x = e2t x(0) = 0, x' (0) = 1 dt2 dt

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Q: y = CLe? + C2 ze? (3) Differentiate with sespect to 'x' get we dy Again differentiate with sespect…

A: Some results are required to understand the differentiation in the given problem.

Q: 3s – 137 L(f) s2 + 2s + 401

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Q: y" – y = 46(t – 2) + t². y(0) = 0, y'(0) = 2. Con

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Q: 2. sin3 350at

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Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = -3.

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Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: Given Answer 1. Se- dx 2. Sxe-* dx 3. Sx? e-* dx

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: L[e-3tcos (3t) + 3e-3tsin (3t)]

A: The solution is given as

Q: 4 -6t laplace (3i*e "cos (t))

A:

Q: x"(t) + 4x" (t) + 9x'(t) + 10x(t) = -24te'; when t = 0, x = 0, x' = -4, x" = 10

A: Use Laplace table

Q: Laplace Transform

A: