Use Laplace Transform to solve यु y=4e ーt %3D given ylo)= 2 and u lo) = -l

Q: у" +у%3D0.001t?, У (0) %3D 0, у'(0) %3D 1.5

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Q: Solve for the laplace transform x(t)= (cosh4t sin4t)/ (te6t)

A: The given function is x(t)=cosh 4t sin 4tt e6t=cosh 4t sin 4tte-6t

Q: find the laplace transform of the equation: f(t)= 2t^3 e^-4t

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Q: What is the period of = sin 4x ? 1 4 2

A: We need to find the period of the function y=sin4x

Q: Apply the properties of laplace transform including the linearity property, shifting property, and…

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Q: i). ƒ (1) = (5– 312) ² i). ƒ (1) =r2sinh (21) Find the Laplace transforms of the following…

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Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

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Q: -2Y dy y°e

A: The given integral is: I=∫y3 e-2y dy

Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: -- solve ÿt y-2y=5é'sint ,y (0)=1 and o)=o using Laplace transforms.

A: We have to find solution by Laplace transform Method.

Q: 2s + 16 s² + 4s + 13

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Q: Find the inverse Laplace transforms: Y(s)=(2s+3)/((s+5)^2+4)

A: 2e−5t(4cos(2t)−7sin(2t))​Explanation:

Q: L{e2"sin2t + etcos3t}

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Q: Consider the function f(x, y) = ax – 2y + 1 where a is a positive number. S SR ax 2y + 1 dA = 45,…

A: A double integral involves the integral with respect to the product of any of two variables in x,y,…

Q: 2) t? t et sin 4

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Q: Use Laplace transform to solve the DE. d²y_3dy = 9 dx² dx where x=0, x=0 and dy=0 dx

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Q: use Laplace trans forms g - 4 y + g'co)= o 3 y = 6t - 8 , ylo)=0 ,

A: Solve the following

Q: 25. Find the general solution of the equation dy = 2y + 2e-. dt (This equation is linear, but please…

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Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

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Q: fnd Invese laplace transform of FA)

A: We have Fs=s2+1ss+12 First we write it in the partial fraction form Let…

Q: Determine the Laplace Transform of est cos 5t .

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Q: Find dy/dx: y = In [(1 + t^2)/(1 - t^2)]

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Q: What would the inverse Laplace Transform be for the attached function if A = 1+j4 and B = 3+j7?…

A: Step 1: Step 2: Step 3: Step 4:

Q: y"+2"-z' = 0 y' + z 221-ex - Yo = 0, y = 1 20= 1, 2 = 1

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Q: Use Raplace Transform to Solue y?+3y'+2y=DUglt) O and %3D guen ylo) =0 y'l6)=1 %3D

A: Use Laplace table to solve this.

Q: infinty use L.23 and L32 of Laplace Transform Table to evaluate Ţ [t] (2t). dt. 0

A: The integralThe Laplace transform of the function f(t)Now, from the Bessel function of the First…

Q: ) 3x - 4x= sin社 ; at t=0,x==

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Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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Q: find laplace Transforms fct) = I+ 7t sin h2t %3D

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Q: 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1).

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Q: (b) 를/ dx 3

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