Use the method Laplace transform to solve the following. (a) 2r' + 7r=3e-t, x(0) = 4. (b) 2r' + 6x=3cos(2), r(0) = 1.

Q: Compute the Laplace transform. Your answer should be a function of the variable s: s(πt)} = c{₁+ +…

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Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

A: We have to find the inverse Laplace transform of the given function.

Q: Q: The Fourier representation of a function f(x): f(x) = {-10 V, 10 V, ーTくX x > 0 40 sinx sin3x…

A: Given f(x) = -10v.  When -π < x < 0              = 10v when 0 < x < π.   Graph of this…

Q: Q.5A/Find Laplace Transform of the following functions 1.f(t) = 6e-6t + +5t3-9 2./(t) = (42marke)…

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Q: Select the correct expression for the Fourier transform of the function f(2)=e-(2+3)³/4 Select one:…

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Q: Given that -9/s cos(9t) L{- Vnt Vi cos(9t). find the Laplace transform of L{V cos(9t)}

A: We find the required Laplace transform

Q: 29. 29. Find inverse Laplace transform of 1 (a) g2 — 38 + 2 )b( - 1 s3(s+1)

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Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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Q: Given that find the Laplace transform of √cos (8t) C{√/cos(8t)} = (-16)^(-8/s)/(88 (5/8)) CL cos(8t)…

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Q: (d) * + 6 + 58x = 116, x(0) = 0, (0) = 1

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Q: Use the definition to find the Laplace Transform of the given function (t, 0st<1 f(t)= OSt<1 1, t21

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: solve: y" - Hý + 4y = 4szt; y(0)=2₁ y(a)=5 using Laplace transform

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Q: A F(s) = S + 5 1 B F(s) = s2 + 25 120 F(s): s6 S + 5 (s + 5)2 D F(s) +

A: We have to find Laplace

Q: Find the inverse Laplace transform L-{F(s)} of the function e-2s F(s) : %D s2 + 5s – 50 NOTE:…

A: Given that Fs=e-2ss2+5s-50 We have to find the inverse Laplace transform of Fs that is L-1Fs For…

Q: using Laplace transform, solve the equation below. y'' -2y' + 2y = cos (t)         y(0) = 1,  y'(0)…

A: To find the solution of differential equation we use the properties of Laplace transform of…

Q: find the Laplace transform of VE cos(3Vf). E{VE cos(3V)} =0.

A: We are given that,  Lcos3tπt=e2.25ss..................................................(1) We are…

Q: 5. Determine the following transforms. b. L{cost 8(t – 37)}.

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Q: Find the inverse Laplace transform f(t) = £¯¹ {F(s)} of the function F(s) = e −3s (1 – 4s) s² + 16

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Q: Solve for the Laplace transform of sint sin 2t cos t

A: The given function is f(t)=sin t sin2t cost  rewrite the function as  f(t)=122sin t cost sin2t…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 2. Find the transform of the equation x² + xy + y² = 1 when the…

A: Let us consider the equation to transform the coordinate use  x=Xcosθ-Ysinθy=Xsinθ+Ycosθ

Q: Using transform ,find the result of the integral x =rcos(0), y =rsin(0) e-(7x2+3y") dxdy

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Q: Exercise (2): Find the inverse Laplace transform of the following functions. 59}. (1) L- (2) L-1 (3)…

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Q: Question #7. Use the Laplace transform to solve x"+x=2t, x(0) = 0, x'(0) = 5.

A: (.)   Given differential equation is ,          x''+x=2t   ;  x(0)=0  , x'(0)=5 (.) Some properties…

Q: ®[6.4] Using the Laplace transform to solve IVP. yu t16y= 43(t-37) H10)=2 , y'0) =0 y10)%=D2 %3D 3D0

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Q: Find a function f(x) whose Laplace transform is e-3p p² +25 You should find f(x) = K sin(R(x -…

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Q: x2, Ixl a

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Q: A point (x,y)=(3,4) is transformerd. First with: [2 And then with: [29] Please calculate the result…

A: Given that , Point x,y=3,4 find the transformed point.

Q: Y(s) = %3D

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Q: 3s+7 B. Find the inverse Laplace transform of F(s) = s(s+1)(s-3)

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Q: · findd the fourier sine transform of f(x) = 7 A 9x 0<X<9 otherwise

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Q: Find the Laplace transform of f (x) = e* sin2x %3D

A: Let us consider a function f(t) then the Laplace transform of f(t) is given as L[f(t)]=F(s) Some of…

Q: Find the inverse Laplace transform L{F(s)} of the given function. 8s2 – 24s + 72 F(s) = s(s² + 36)…

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