Q3.The following equation models a spring that receives an initial shock and then an aftershock half as strong 5 units of time later. 1" + 4x' + 20x = 26(1) + 6(t – 5), r(0) = 0, x'(0) = 0. What is r(6)? e10 sin(4) + 2 sin(24) b) he2 sin(4) + 2 sin(24) e10 sin(4) + 2 sin(24) 4e12 e10 sin(4) + 2 sin(8) d) 4e12 4e12

Q: The motion of a mass on a spring is described by 3y" + 4y = 0, y(0) = 5, y'(0) = 6. What is the…

A: Given:The motion is described by 3y''+4y=0, y0=5, y'0=6. We have to find the amplitude of the…

Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: Find f. a) f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 8   b) A particle is moving…

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Q: 8) A particle that moves along a linear path has a known velocity of v(t) = 4.3 sin (2.1t), where…

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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: Solve the IVP y"(1) +y'(t)- 2y(1)= 2e' sin(t), y(0) = 1, y'(0) = 1. %3D

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Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

A: The objective of the question is to solve the given second order differential equation with the…

Q: dy If y = sin-(e*), then dxlx=ln( (a)v8 (b) cos™*() (c)- T3 (d) ;

A: Given that: y=sin-1(ex)

Q: 54. Let D be the region bounded below by the cone z = Vx² + y? and above by the plane z = cal…

A: To determine: The triple integration for the region bounded below by the cone z=x2+y2 and above by…

Q: Show that the following equations are exact. Find solution. (a) dx dy_x– y³ + y² sin x 3xy² + 2y cos…

A: (a) The differential equation is given as dydx = x-y3+y2 sinx3xy2+2y cosx It can be rewritten as…

Q: 1. Solve y"+9y=0 subject to the initial conditions y(0) =1, y'(0)=-1. Use Euler's Formula: e* =…

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Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Find a particular solution to /" + 16y = 8 sin(4t).

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Q: (D² + D)y = 81r² +14 cos(4x) where y(0) = 0 and y'(0) = 3 %3D

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Q: Please

A: We use MOUC to solve given differential equation.

Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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Q: Find the general solution:

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Q: Part IV. Solve the given problem. Show your solution. The electronic force for an electric circuit…

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Q: y" + 9y = e²* sin(x)

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Q: (i). y' = 1 + 3y tanx Ans. 3y cos³x = c + 3sinx - sin³x

A: this is a linear differential equation. solve it using integrating factors.

Q: (c) y" + 2y-3y = 9 sin(t)

A: A detailed solution is given below

Q: 4. y=sin(3x) • cos(2x), y'=?

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: y" + 3y² - 2 = e².sint (Variation of parameters)

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Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: the solution to the given equa y" + y' – 2y = cos(x) – 3 sin(: -

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

Q: A mass that weighs 8 pounds stretches a spring 6 inches. The system is acted on by an external force…

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Q: (1+x)y' + y = cosx; y(0) = 1

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Q: If y(v) = 10 COS 79 72 dr then

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Q: Slve the Following initl Value Problems s- a) V+4Y=20 (y=2), b)y'= 2(V-1) tanhx (YCO) =4), c)Y'+3Y=…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

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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.