(c) The displacement, x, of a particle in simple harmonic motion is given by x = cos(3t) – sin(3t). Show that d²x + 9x = 0 dt2

Q: The position of a moving particle as a function of time is given by: x = (4 - 0.1t) sin(0.8t) Plot…

A: Hi! You have posted multiple questions. As per norms, we are solving only the first one. If you need…

Q: 4 T 40 sin(3x)dx None of them -0.532 -0.253 0.253 -0.235 0.0235 -0.325

A: Solve the definite integral

Q: Consider the forced linear harmonic oscillator y" + w?y = cos wt where the frequency W = 4 Find a…

A: We are given that y''+ω2y=cosωtwhich can be written as (D2+ω2)y=cosωt.We have to find particular…

Q: A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4…

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Q: y = c, e2* cos 3x+C, e²* sin 3x

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Q: 0 16) cos t dt dx

A: Given:

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: d 27. dx ], cos t dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

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Q: dy 5- + 4y = 4y¯te-2 Solve the DE CoS r. %3D dx

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Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

Q: sec x dy - 4 sin x sec y dx = 0

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Q: 3. Eliminate the Arbitrary Constants (C, and C2) in the equation. (25 pts) y = C,cos (At) – C2 sin…

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Q: *10. cos Z = 0.5234 YX _ y 24

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Q: Find the general solution of the following equations. 4. dy - x² = x dx sin x 5. y-'dy + ye cos x dx…

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Q: B-The result of dy/dx for the following function is COS X y 1+sin x

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Q: The acceleration ā of a particle at any time t is given by à = e-2 î + 3t ĵ+cos t k , then the…

A: The acceleration of a particle is given by a→=e-2t i^ + 3t j^ +cost k^  v(t) = ∫a(t) dt = ∫(e-2t i^…

Q: BERNOULL니 dx -X = x siny dy ANSWER; hus -) § losy + Ce) X= -

A: dxdy-x=x3/2sinyx-3/2dxdy-x-1/2=siny                        1 Substituting x-1/2=v…

Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: Find the linear approximation to f (t)= cos(2t) at t =1/2. Use the linear approximation to…

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Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: d. t sin 2 dt COS dx 3

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Q: 1) The value of f t.e-3t. sin 2t dt

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Q: Solve the Bernoulli's equation given below: dy -ycot 2x dx 3 CSC 2x ( )」 Sn 2メ= ーメキC a. C-2) Sin 2x…

A: We have to solve the Bernoulli's equation  By convert Bernoulli's equation in First order linear…

Q: 1. Consider 3x + sin x – e* = 0, using Secant Method with initial points xo = 0 and x1 = 1,…

A: The given equation is; 3x+sinx-ex=0.

Q: Consider the forced linear harmonic oscillator y" + w?y = cos wt = COS where the frequency W = 3…

A: The given Differential equation is  y''+ω2y=cosωtwhich can be written as (D2+ω2)y=cosωtGiven that…

Q: et cos(e') dt = (b) +C 3+4 sin(et) 3/4 sin-1 (c) (승교) dx = 16x?

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Q: (a) e 20 sin(30) de (b) t sin(2t) dt 0.

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Q: Solve the Bernoulli's equation given below: dy 2 dx -y cot2x = y' csc2x O A. [(y )^(- 2)] sin 2x = -…

A: Use Bernoulli theorem to solve

Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: 1- y" - 6y' - 7y 2 cos Dt sin Mt Find Particular solution

A: It can be solved by finding C.F. and P.I

Q: 4. Solve for in the equations below: dx a) -1 dy y? dx b) cos x – sin y 2 = 2- 3 ) xe+ e = 3"

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Q: A weight is attached to a spring suspended vertically from a ceiling. When a driving force is…

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Q: (5) (2x – y) = 2y – x | dx (6) (02 + 1) cosr dr + 20 sinr de = 0 %3D

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Q: 1. Please answer the following questions. a) [x-In (4x²) dx b) ſe* *. cos (2x) dx c) [In (x² +2) dx…

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Q: c) Se- sin(4t) dt

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Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

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Q: d Cvaluate dx cos (r² + 1) dt

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Q: A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its…

A: given velocity of the particle at time 't' v=3t2i+2cos4tj+t2k initial position x(0)=2i

Q: 1/10 1.A) e* cos(5x) dx integration by parts

A: Here we have to do integration by parts:   Apply integration by parts u as e3x and v = cos5x

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

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Q: D. ( [ 3° cos"(5t) dt sin(z)

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