Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: dz Find given: dt =ze, =t', y= 5+5t dz dt

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Q: dx + dx dy e; dy = x +y Use elimination to solve: dt dt dt dt

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Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? ... (2) ev²…

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Q: w = xy, x = e", Given Find dw/dt

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Q: dx If y = 2x3 + 3x and dt dy 3, find when x = 4. %3D dt dy dt =

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Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: 2 dy = t(i+t=) sec>x dt

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Q: The radius r and height h of a right circular cylinder are related to the cylinder’s volume V by the…

A: It is given that, the height (h), radius (r) and volume (V) of a cylinder are related by the…

Q: If x2 + y? + z2 = 9, dt dy = 9, find dt dz when (x, y, z) = (2, 2, 1). = 4, and %3D dt %3D

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Q: da dy 3x? – 1 and dt Find at z = 1 if y = at x = -5. dt da dt

A: topic - derivative of a function

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Find the solution to dy/dt = 6y Satisfying y(1)=7 y = ?

A: Firstly , separate the variables and then integrate and solve. ∫1ydy = ln(y) +C ∫tn dt =tn+1n+!+C

Q: dy Find - given that dt dx x + y? = 3x + 5y, x = 4 y = 1, and 9. dt dy dt II

A: As we know that the chain rule: dydx=dydt×dtdx The Power rule: ddxxn=nxn-1 Given: x2+y2=3x+5y…

Q: 2. Assume w=xy* , where x and y are functions of t. dw Find dt dx =2, when x=3, dt dy - 4, and y=1…

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Q: Evaluate dx f(t) dt and * f(t) dt, where a and b are constants.

A: To evaluate: ddx∫axft dt and ddx∫abft dt, where a and b are constants. Solution: The fundamental…

Q: tan x d. y = sec? t dt 3 е. y = dx 1— х2. its

A: We have to find dy/dx for the given function

Q: dy Find given that dt dx x + y = 2x + 4y, x= 3 y = 1, and %3D = 6 dt dy %3D dt

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Q: If z = x? + y with z > 0, dæ/dt = 4, and dy/dt = 6, find dz/dt when a = 4 and y = 3. dz Answer: dt

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Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

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Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: Solve the DE using homogenous equations: Let: x = vy dx = vdy+ydv xy dx - (x2+3y2) dy = 0

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Q: Find the general solution for y(t) where; dy a. dt + 6t?y = 2t2 dy b. + 10y = 0 dt

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Q: da dy at z = – 5 if y = 3x2 – 3 and - 1. Find at x = %3D - dt dt dx %3D dt ||

A: given y=3x2-3 ........(1)

Q: Find dy/dx: a. y = cos t dt 0,

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

Q: dx dy 1. " + y = x , dt = 3y dt |

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Q: Find dy/dx: 1. y = J" cos t dt

A: Given

Q: dy Find -given that dt dx x2 + y? = 2x + 4y, x = 3 y = 1, and 7 dt dy dt

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Q: Find an interval where the IVP dy (In t) + y = cot t dt y(2) = 3 has a unique solution.

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Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

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Q: Find the general solution to dx = x + y – z dt dy 2y dt dz = y – z dt

A: Given,  dxdt=x+y-z . . . .. . . .1dydt=2y . . . . . ............2dzdt=y-z . . . . . . . . . . . 3…

Q: dz Find given: dt Z = xe?", * = t“, y = 5 + 6t dz dt %3D

A: Put value in terms of the then differenciate

Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: Find the general solution for y(t) where; dy а. dt + 6t?y = 2t? dy b. + 10y = 0 dt

A: The given question has been solved in detail

Q: dz + et+z = 0 dt

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Q: Find given that dt x² + y² = 2x+4y, x = 3 y = 1, and dy dt i dx dt

A: SOLUTION-

Q: dy Find - given that dt dx x2 + y? = 2x + 4y, x = 3 y = 1, and 7 dt dy i dt

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Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: Find fa and fy. f(x, y) = 4e dt %3D

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Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

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Q: Find dz/dt dz/dt given:  z=xe2y, x=t6, y= -1+5t

A: Given,         z=xe2y    , x=t6     ,    y= -1+5tWe know that,            ∴dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: O1f y= x 4x and x = Vzr?+I, find dy /dt when t r2. %3D

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Q: d?x dx + 4 + 5x – 10 = 0, when t = 0,x = 0,x = 0 %D | dt2 dt

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Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: dz 2) Find if z = xy² + x?y, y = ln x %3D dt

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Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

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