Solve by the Laplace transform, showing the details y" + 10y' + 24y = 144r², y(0) = 19/12, y'(0) = -5 %3D %3D %3D

Q: Evaluate 3 | ((2 – 1)32, (3 + t)2, 1)dx. 3/2 3/2 -3

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Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: Solve equation using Laplace transform ÿ + 9y = 8 (t -) |sin(t), y(0) = 0, ý(0) = 0

A: Formulae:  1. Lf(t)δ(t-a)=e-asf(a) 2. Lf''(t)=s2F(s) - sf(0)-f'(0) 3. L-1e-asF(s)=H(t-a)f(t-a),…

Q: V3/2 1 dx%3D 6). V1- x 1/2

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Q: Laplace transform of f(t) = e(4t-8)cos3(8t)

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Q: x dx Using Beta and Gamma Evaluate 5*

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

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Q: Find dy/dx. y = __2x + 3)3__ (4x 2 − 1)8

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Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

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Q: F(@) = ? -1 f(t) 1

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Q: y' = e2x + y – 1

A: Using method of linear differential equation.

Q: Evaluate 4x cos(2-3x) dx

A: Given: The objective is to evaluate ∫4xcos2-3xdx.

Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: To evaluate: The integration of ∫sin2x·cos 2x1+cos 4xdx. Formula used: Trigonometric relation: 1+cos…

Q: 1/3 + 4y/6 = 2/3 Show your work

A: The given equation is 13+4y6=23To solve for the value of y

Q: dx x√3x² + 2x - 1 - arcsin 1-x 2x +C (Hint: Let x = 1/z.)

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Q: Find the Fourier transform of the following function: 7 sin(3r – 2) r2 + 25 - 2 exp (4 - 5|r-3|).

A: We are given a function in variable x and we have to find its Fourier transform. For that we will…

Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: Find the inverse Laplace transform of the function F(s)= (s- 4)e^-3s/(s^3 + 4s)

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