7. The velocity of an object traveling along a straight line is v(t) = cos(t) + 4t + 1 meters per second. At t = 1 second, it is located 4 meters to the left of a post located at a = 0. (For this problem, leftwards is the negative x direction and rightwards is the positive x direction.)

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Q: 9. The position of a moving particle as a function of time is given by: x = (4 -0.11) sin(0.81) Plot…

A: The given position of moving particle is, x=4-0.1tsin0.8ty=4-0.1tcos0.8tz=0.4t32

Q: 2. Solve the following initial value problem. dy = sin(Tx) dx? y/ (1) = y(1) = 0. - -

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Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

A: The position at time t ≥ 0 of a particle moving along a coordinate line is s = 10 cos(t + π/4) We…

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A: Solve the given

Q: 4. Find the General and Particular solution of dy -8 sin 4x ; y = 6 when x = 0 dx dy

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Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

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A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: Solve the initial value problem. 33) dy - et sin (et – 5), y(ln 5) = 0 dt A) y = sin et - sin 2 C) y…

A: Given initial value problem can be evaluated as shown below by using substitution method

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: 2. Find a particular solution using Undetermined Coefficients to: y" + 2y' – 3y = f(t), where f(t)…

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: 4) It turns out the three-dimensio ball than a football. A footba a trig function like y = a cos(E…

A: Volume

Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: Given the function y=sinx-2 for 0°<xS180° 5.4.1 Draw the graph on its own system of axes on the…

A: According to question,Given function,y = sin x -2,where,0o ≤ x ≤ 180o,

Q: A particle moves along the x-axis with position given by x (t) = -2 cos (2t) + 2 for time t > 0.…

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Q: 1. Solve (cosxcos y+2x)dx-(sinxsin y+2y)dy=0

A: (cosx cosy + 2x)dx - (sin x siny + 2y)dy = 0 =&gt; cosx cosy dx + 2x dx - sin x siny dy - 2y dy = 0…

Q: 4. The velocity, v ms-1, of a fairground ride t seconds after it begins is given by v = (3et + 7)sin…

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Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

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Q: If we neglect air resistance, then the range of a ball (or any projectile) shot at an angle θ with…

A: Given,

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

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Q: 5. Consider the equation: 3x – 2 cos x = 0. Use Newton's method starting with the initial…

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Q: Solve the initial value problem: cos z – 3x?y – 2æ) dx + (2y sin x – x° + In y) dy = 0; y (0) - -- -…

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Q: () = 2 + Solve the initial value problem : f'(x) = cosx + sec?x, %3D

A: As you post multiple questions we only solve first question only.

Q: 5. Find a general solution to the following nonhomogeneous equation: 1 y" + y' cos t sin t Hint: S…

A: Third order non homogeneous differential equation.

Q: 1. S8te7 dt 2. "(1 – 3x) sin Gx) dx -2n L w²e*wdw 3.

A: Given, Simplify

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Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

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Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). When…

A: Given,The position at  time t ≥ 0 of a particle moving along a coordinate line is s=10 cos(t…

Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

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Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

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Q: Solve the following initial value problem. y(4) = - 2 sint+3cos t with y'''() = 8, y"(0) = - 3,…

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Q: Solve the initial value problem.

A: To solve the initial value problem.

Q: 8. Suppose that the tangent line to the graph of ƒ(x) = r0) at r = 1 is equal to the tangent line to…

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Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: The linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is:

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Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: Suppose the velocity of a particle at time t is given by 3/19 (t+1)2 + V+1 1 7(t) (tan(t). 1+12 1.…

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Q: A particle moves along the x-axis with acceleration given by 5T sin (at) for time t > 0. If the…

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Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: 4. A particle that moves along the x – axis has velocity v(t) = t² sin(2t) at time t seconds. a) If…

A: Given data: The expression for the velocity of the particle is v(t)=t2sin(2t).   a) The initial…

Q: 7. A particle travels on the x-axis so its velocity at time t is given by v(t) = ÷- sin t, for 0 <t…

A: In the question it is asked to calculate value of time t for which the particle moves to the right.

Q: d'y dy dx² dx 21 29 - -6y=6e¹ cos x; when x=0, 20 dy dx =-629 y = 2e-3x - 2e²x 3e-* 29 (3 sin x - 7…

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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