Which of the following expressions' inverse Laplace transform is the solution to the initial value problem I" – 3x' + 2x = 6, x(0) = 2, x'(0) = 6 ? %3D

Q: Find ay dt + = -1 (+-√e ³ sin ¹ (2+) 1(5+2log +) 9

A: We will use the formula ddtmn=nm'-mn'n2

Q: (s) = (1-3s) / (s^2+8s+21) A [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(-4t)] + [3*cos(sqrt(5)t)*e^ B…

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Q: By expressing the product as a sum, 2cos(3x)cos(4x)= ?

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Q: (A) Evaluate Sin (3x) Sin (3x) dx

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Q: If F(s) = -3s² s + 1 is the Laplace transform of f(t), find the following, correct to three decimal…

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Q: Let f(x) = x/x), (0<x<10) then Fourier coefficient a20 has value when an even periodic extension is…

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Q: Question 3 4. a) Integrate tan (0) sec (0)d0.

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

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Q: NO i need it to be the Fourier transform as X(jw). Dont use this as s tranfer functions  I dont…

A: Let us go through the subpart (b) whose integral to be evaluated is .The graph of the function with…

Q: 1- cos t Find the Laplace transform of

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Q: dt cos (2 sin 21) /1– 4r

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Q: f indd Pm in tev ms of @m-l and @gtl n+l -ax dx m,n-1 dx I. Cm, m-l= Hint: Recursive Method Matrid…

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Q: QUESTION 5 (3 points) Find dy/dt. y= cos(/10+12) 5 -sin 10+12 5 sin(10t+12) 10t+12 1 sin(10t+12)…

A: Kindly see attached photo for your guidance.

Q: 더 - C 1 -2s +6 s+2 82 - 4s + 8+1 C S-2 1

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: 70. Which of the following. is the inverse Laplace transfor B (B^2-9)/(s^2+9)^2 ? A. cos (3t)+3t…

A: The given expression for the inverse Laplace transform is:The objective is to determine which of the…

Q: Solve the following ODE * (y sin x + xy cos x) dx + (x sin x+ 1) dy =0 1 Add file

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Q: SOLVE THE FOLLOWING ODE STEP BY STEP IN DIGITAL FORMAT PLEASE 4y = (y')² - 4 xy' + 2y = sin y

A: Since you have asked multiple questions here, we will solve the first one for you. To get the…

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

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Q: (a) sec¹ (31) √tan(3t) dt

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Q: How to solve the Laplace transform of the following equation: W(t)=cos(3t) - cos(7t) Please write…

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Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

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: Prove that the Dirac delta function satisfies +∞ 1 S(t – t') = 2/= t 2π ģ exp(-iw[t − t']) dw,

A: First recall the definition of Fourier transform and inverse Fourier transform of a  function The…

Q: 5. (Ci | Show that L{e"t"} = n! in two ways: (s- a)n+1 (a) Use the translation property for F(s).…

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Q: 1/2 Evaluate csc лt cotët dt [ 1/6

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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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Q: 1. Find the laplace transform of 2e^(3t) sin 4 t 2. Simplify i²⁹ + i²¹ + i 3. Write in the form a…

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Q: -2 dæ [(ax)? – b°]3/2

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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.