Which of the following differential equation(s) is/are NOT applicable for the method of Laplace transform? I : 4y" + y = t=1/?et +e2t, II : y" – 2y' + y = U»(t) + e² – 1 III : y" + y' + 3y = t=?e5t cos t A)Only I B) Only II C) I and III D) II and III E) Only III

Q: Q"+4Q'+4Q=2t Solve with Laplace transform

A: Using laplace transform to solve the problem.

Q: ikt 三 ik ik Ikt. ik こ

A: So we have to solve the inverse Fourier transform to get the expression for U(x,t)

Q: Consider any(n) + an-1y(n-1) + + a1y' + aoy = f(x) where an, ...a1, ao E R, where an 7 0. ... (a)…

A: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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Q: O For the differential equation -at y" + 2y'- 3y = 6e Determine the solutioo using Laplace t theorem…

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Q: 4) Using Laplace transform to solve y" + 9y = cos³t, yco)=1, y'co)=5 Hint: ду Lr sinkt + Ktcoskt}…

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Q: Determine the constants a, p, yo and y'o so that Y(s) = Bs + C (s + D)² is the Laplace transform of…

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Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –…

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Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

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: (i) B(2,3)-

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Q: 1) x(t) = 1(t- 47T)

A: Solution 1: Given function is x(t)=1(t-4T)           (1) Let the z-transform of x(t) is X(z)…

Q: What is the inverse Laplace Transform of a function y(t) if after solving 32-s+3 Differential…

A: Given To determine inverse Laplace transform of a function y(t) Using inverse Laplace transform…

Q: se-2s -)=D 's²+45+3

A: Given,

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: Perform the following Laplace transform 1) f() = (t+(2)? -2 Cos (2)t)

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Q: Determine the Laplace transform of y’’ given y (0) = 4 and y’(0) = 2

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Q: Use Laplace Transform to solve the differential equation: d'y dt + 4y = 1- Subject to y=-2 and- 1…

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Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 F₁ (t) = −6(t + 2) +…

A: What is Dirac Delta Function: The unit impulse, sometimes referred to as the Dirac delta…

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: dt? + w?) G(t) = 6(t) () 1. Now using the Fourier transformation on both sides of equation 1 and…

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Q: Consider this ordinary differential equation (ODE): dy da At the point (-0.5, 1.5), the direction…

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Q: Find the Fourier transform of the function y(t) if y(t) satisfies the differential equation d°y_dy…

A: First note that:  F-1e-5ω=12π∫-∞∞e-5ωejωtdω                       =12π∫-∞0e5ωejωtdω+12π∫0∞e-5ωejωtdω…

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (5 e' cos…

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Q: 6. et+7 dt 7. r'e-)* dt 8. I. 4e-" sin 6t dt

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: The region bounded by f(x) 2x² + 12x + 14, x = = 0 is rotated about the y-axis. Find the volume of…

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Q: y = tan o (sin 67E-TT) find dy dt ()

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Q: By using Laplace transform to solve y"-y e' with y (0) = 1 and y (0) = 0 ,what would the particular…

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Q: y"+y' = 0; y(0) = 0, y '(0) = 1 cost + sint t + cost + sint A) 1- e-t t-e-t O

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Q: у" — 4y' + 13у %3D е2х сos 3x

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Q: 2) x' + y' + x = 0 ve x' + 2y' = 1 system of equations x(0) = y(0) = 0 Laplace under initial…

A: Given below the detailed solution

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.