x' (t) + 4x' (t) = −2t – sin(t – 4), with x(4) = 0, and x'(4) = 1.

Q: 2(s-3) L-1 s²–6s+13) (ix) 3s+2 (x) L- (s2-8s+25)

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Q: 3. Find the Fourier transform of of 1/(1+t²).

A: Let  g(t)=e-at Then g^f=∫-∞∞e-ate-2πiftdt      =∫-∞0e-ate-2πiftdt + ∫0∞e-ate-2πiftdt…

Q: Use the tables of Laplace Transforms to find the inverse Laplace Transform : F(s)= 2 s² +35-4

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

Q: Use the tables of Laplace Transforms to find the inverse Laplace Transform: F(s)=|-e

A: Given Laplace transform is Fs=1-e-2ss2

Q: (iii) L-1 (3s-1. 5 (iv) L-

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Q: Use the table of Laplace transforms to find the following Laplace transforms. Use s as your…

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Q: 1. Problem Solving. Solve the following problems completely. Use additional short coupon bond for…

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Q: 11. Consider the differential equation dy dt (a) Show that the constant function yı(t) = 0 is a…

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Q: - f(t) = teat sin bt

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 1. Find the transform of the equation 3x+2y-5= 0 when the…

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Q: Find the inverse Laplace transform of F( where 1 F(s) = s(s? + 2s + 2) %3D

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Q: Find the Laplace transform of f () = a2. Answer: 3 a. b. C. d.

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Q: (vii) L-1_2(s+1) ls²+2s+10)

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Q: Use the table of Laplace transforms to find the following 99 L 84

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

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Q: 4s (v) L-1 s²–16) 2 (vi) L- ((s-3)5)

A: By using the table of Laplace transform we solve the given problem as follows :

Q: 2 5. f(t) = e-²t (t³ + 1)²

A: Some of the formulas of Laplace transformation . Ltn=n!sn+1Leat=1s-aLeatf(t)=F(s-a), L[f(t)]=F(s)

Q: s2 + 6s + 8 G(s) = s4 + 8s2 + 16° xnlanation calculation IS we

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Q: M= 2 Solve the following difference equation by using Z-transform by replacing the value of M as per…

A: Given that,yk+2-2Myk+1+M2yk=M 2ky0=0, y1=MFor M=2,yk+2-22yk+1+22yk=22kyk+2-4yk+1+4yk=2k+1y0=0, y1=2

Q: -3iw sin 5w 20e F(@) = %3D 3

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Q: Q4: Find the inverse Fourier transform of the spectrum: - 2s w S0 X (w) = 0 swS2 -- 0.W EIN I 0

A: Definition:

Q: This is a two-part question. (a) The correct form for the partial fraction decomposition of 4+5+45…

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Q: L-1(1/(s4+4))

A: L-1s+1s+12+1=e-tcost L-11s+12+1=e-tsint L-1s-1s-12+1=etcost L-11s-12+1=etsint

Q: Solve The Differential Equation Step by Step 4t²x" + (t²+1)x=0

A: Given differential equation is 4t2x''+(t2+1)x=0         (1) Let the solution be x=∑antn+m Then…

Q: Laplace transform of the following functions: 2. t5/2 sinh 4t

A: We find the Laplace transform of the given function in Problem 2

Q: can someone help me find the inverse of that laplace LEYCA'S = 5/11 (5²-6315) + $-6375 2 (5-11²

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Q: Solve the following Laplace Transform of Algebraic Expression: 5. Finf the L t?e-3t ? Show Solution.

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Q: f) = (ae aet t<0 3) Find Fourier Transform for the following function as in figure:

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Q: (b) Sketch the following function. Write down its equation in unit step function and find its…

A: Given

Q: = f(t) = t6 — 4t² +5 -

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