16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of time t. How is dt if the radius of the cylinder is constant?

Q: 1 5 X If y = - find dy dx at x = 2.

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Q: Hi, can I get help with this problem? Thank you! 4.1

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Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Given differential equation is: ydydx=x−1;  y1=0

Q: 14. A particle moves along the x-axis so that its acceleration at any time t is a(t) = 2t - 7. If…

A: Given that, A particle is moving along the x-axis so that its acceleration at time t is a(t) = 2t…

Q: Example 10.14. Apply Runge's method to find an approximate value of y when x= 0.2, given that dy/dx…

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Q: Example 10.15. Apply Runge-Kutta fourth order method to find an approximate value of y when x = 0.2…

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Q: 1) Find dy/dt for if : y = log2 (87ln 2)

A: Apply differential rule to solve 1st question [ln(u(x))]'=1u(x)u'(x) power rule [x(n)]'=nxn-1 Apply…

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A: The example of birthrates should follow Poisson's distribution where λi are the birthrates, since…

Q: Suppose The problem of intial values y = log (x+y), y(a) = 2 How often is. The modified Euter method…

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Q: The solution of the following logistic equation is dy = ry (11 –):y (0) = k %3D dt 13 1 ellrt 144 Y…

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Q: Suppose that a certain population obeys the logistic equation dy/dt = ry(1 − (y/K)). a.If y0 = K/3,…

A: (a)calculation:

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the…

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given…

Q: 3. Sketch solution curves for a variety of initial conditions for dw = (w - 3)(w – 7). dt

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Q: Suppose that we are interested in the amount of salt (in kg) at a certain moment in time, denoted by…

A: To solve the given statements

Q: Solve the initial value problems for x as a functionof t. (t + 1) dx/dt = x2 + 1 (t > -1), x(0) =…

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Q: Question 3. Prove that L(e^)(«) = * & dt.

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Q: If y approximate the differential dy when x changes from 64 to 64.07

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Q: 1) Find dy/dt for if : y = log2 (81'n 2)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve the following IVP: dy dt? dy 6. + 9y = e dt 3t

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Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

Q: 1 So 2t en + e-2t ezt - e-at dt

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Q: 4. If a point is moving along y = 3x2- 4x – 6 at a rate of = 4 m/s, find dt when x = 3.

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Q: 1- S7 cos(y)eSin(y)+9X dydx

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Q: Solve the following initial value problem: dy + (0.9)ty = 5t dt with y(0) = 8. (Find y as a function…

A: Re-arrange the differential equation.

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Suppose that y(x) is a function satisfying the following initial value problem: 2 dy = a² + 9/ , da…

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Q: Find dy/dxin terms of x and y if ax^4−by^4=c^4 Assume that a, b and c are constants. dydx=…

A: Given : ax4-by4 = c4 a, b and c are constants. To determine dydx

Q: Let e 2* = 2 find dy dx at x = 1

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Q: Find So S 4:xy dx dy.

A: Evaluate the integral.

Q: Show X -メ+1 =ソ- Can be reduce d to homegenons equation 2X +y-! メ+ 2y t1 dy dx

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Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

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Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Let A and k be positive constants. What is a solution to dy/dt=k(1-Ay)

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Q: Solve the following initial value problem: (dy/dt)+(0.2)ty=4t with y(0)=9. (Find y as a function of…

A: First simplify the given differential equation and write in the form of standard homogenous…

Q: 2. Solve the following problem 10 (хи — 2x2 — 5и?)dt max | 0, dx = x + 3u, x(0) = 6, x(10) free dt

A: We will use Euler-Lagrange equation to solbe the optimization problem.

Q: →Solve the following problem. (441)- max f = | (2x + u)dte dx = 5 – u², x(0) = 1, x(2) free“ dt

A: The complete solutions are given below

Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Suppose we have a pendulum clock that uses a slightly damped pendulum to keep time (that is, b is…

A: At first we will derive a direct relationship between θ and m then from that we will observe how θ…

Q: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

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Q: Example 10.33. Applying Euler's method to the equation dy/dx = hy, given y(x) = yo determine its…

A: We need to solve this problem using Euler's Method.

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Solve the following initial value problem: dy + y = 49t dt with y(0) = 6. (Find y as a function of…

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Q: 1) Find dy/dt for if : y = log2 (81n 2)

A: