x'(t) = 2 x(t) – 3 y(t) ; y'(t) = y(t) – 2 x(t) doğrusal diferansiyel denklem ninin x(0) = 0 , y(0) = 3 Başlangıç koşulları altındaki bir çözümünü Laplace Dönüşümü emi ile elde ediniz.

Q: = Find the inverse Laplace transform f(t) = L-¹ {F(s)} of the function F(s) = f(t)= [38+4 +36 = L-1,…

A:

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: Solve the Laplace Transform of the equation f(t)= sin3t/t

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Q: use laplace transform to solve y'-y=2cos(t), y(0) = 4

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Q: Describe in your own words the method you would use to find the Laplace transform of the first…

A: The Laplace transform of function f(t) is given by Lft=∫0∞e-stft dt and is denoted by F(s). We can…

Q: ,3t sin4t 2.- t

A: Laplace transform

Q: Solve the initial value problem using Laplace transform y" – 4y'+4y= 3te", y(0)=4, y'(0) = 2

A: The given question is related with Laplace transform. Given that,                    y'' - 4y' + 4y…

Q: 1 -s F(s) = e = -+ s2 e-3s

A:

Q: 14. x" + y = -101 sin(10t) ; y " + x = 101 sin(10t) ; x(0) = 0, x ' (0) = 6, y(0) = 8, y' (0) = -6

A:

Q: (t +1)² 0 3

A: Given that yt=t+120≤t<3t+22t≥3 Then by definition, Lyt=∫0∞e-sty(t) dt=∫03e-stt+12dt+∫3∞e-stt+22dt…

Q: Find x(t) and Y(t) using Laplace transform.

A: The given pair of equations dxdt=2x-3ydydt=y-2xx0=8, y0=3

Q: Let f(t) = e^t if 0=1   Write f(t) using step function and find the laplace transform. Also,…

A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

Q: y" + 2y' + 5y = 10e¬2", y(0) = 0, y'(0) = 0.

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Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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Q: t3 - 3t2 + 5t – 8

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Q: use the Laplace transform to solve the initial value problem.

A: It is required to solve the initial value problem using laplace transform:

Q: find the fourier transform of logx u(t)

A: Unit step function: u(t)=1t≥00t<0 Fourier transform of a function fx is  Fp=∫-∞∞fteiptdt…

Q: In a equation, f(x) = 3 sin 3x - 2e-2x Calculate the Laplace transform

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Q: y" + 3y/ + 2y = e-t, y(0) = 0, y'(0) = 2.

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Q: x^2y′′ + (3/2xy′ + [(1/36)x^2/3 − 7/144]y = 0 z = (1/2)x^1/3, w = yx^1/4 Solve it using the…

A: The transform method can be used to find the solution to the differential equation x^2y′′ + (3/2xy′…

Q: f(t) A 10 0 2 4 6 t

A: We have to solve given problem:

Q: Find the Laplace transform of the given periodic function 0<t<1 f(t) 1<t< 2

A: Given ft=00&lt;t&lt;1t1&lt;t&lt;2

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

A:

Q: Find Fourier transform for the following functions:x(t)=3+(sin2wt)2

A: Given function is, xt=3+sin2wt2.      ........1 Fourier transformation: Fourier transformation of…

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: Determine the transform of the following functions using any methods . e^3t sinh 3t

A: Given function is e3t sinh3t

Q: Solve the laplace transform 3x-6x= Sin 2t %3D given when t=0

A: Use the laplace transformation table and derivative formula

Q: Find the Laplace transform F(s) = f(t)= (3-t) (h(t-4)-h(t-6)), for a 0. F(8) = C {f(t)} 2h(3-1)/s^2…

A: We know for a function g(t),           L{g(t)h(t - c)} = e-cs L{g(t + c)} Here, h(t - c) is…

Q: Use formulas from this course to find the inverse Laplace transform (a) L-1{+1) 2s+1 1 252+8 (b)…

A: Solution:

Q: Find the convolution of f(t) = 3t and g(t) = sin (21). You can either calculate f * g directly, or…

A: In the given problem we have to find the convolution of two function f(t) and g(t) using the…

Q: f(t) =sin 4x/x. Find the Laplace transform

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Q: Find the Laplace transform of sinh3 4t

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Q: A piezoelectric transducer has an input Solve the differential equation to find e. For t = T-, find…

A: From the given information:

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

A: