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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A: Solve the following

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Q: 1. Solve the DE as follows: d'y dy +3. +2y = 24 y(0) = 10 and y'(0) =0 dt? dt

A: Note :-  As per our guidelines , we will solve only first question for you. If you want any specific…

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A: An autonomous first-order ordinary differential equation is an equation of the form

Q: (a) x = 0: dy/dt (b) x = 2: dy/dt (c) z = 3: dy/dt

A: Given that x2+y2=25, and dxdt=6 we have to find dydt when y>0 and  a) x=0b) x=2c) x=3 Important…

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Q: Solve IVP: dx x + Y, (0) = 0 dt dy 4x + Y, y (0) = 3. dt

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Q: If L = √(x2 + y2), dx/dt = -1, and dy/dt = 3, find dL/dt whenx = 5 and y = 12.

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Q: If x^2+y^2=36 and dx/dt=9, find dy/dt when y is positive and (a) x=0: dy/dt= (b) x=2: dy/dt=  (c)…

A: Given: x2+y2=36    -1⇒y2=36-x2⇒y=36-x2   -2dxdt=9   -3

Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, and y = ln (t + 1).

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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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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A: topic - derivative of a function

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A: Differentiate wrt  t

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy dx + x + 4y = 10; æ dt - y = 0 dt

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Q: Integrate the following (a )∫eπ31cos (lnt)/t dt   and   (b) ∫2y−11/ y^2−y−6 dy

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Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: If x2 + y2 + z² = 9, xp 6, and dy = 9, find dt dz when (x, y, z) = (2, 2, 1). dt dt dz dt

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Q: Find da d.t da dt at x = 4 if y = 4x² – 1 and > Next Question dy dt = - 5.

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Q: What is an integrating factor of the DE dy/dx = (y + y^2) / x ?

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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: *show work*

A: Find dy/dt.

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Q: Question 1

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Q: Find dy/dt using the given values. y = x - 3x for x = 4, dx/dt = 4. dy dt

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Q: 3 a) Find the exact integer value of a for which tsin (at)dt == ft sin (xt) dt = -². where a1. T

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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: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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A: Topic = Derivative