If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

Q: Calculate the total differential of: a) z = 3x² + xy-2y³ b) z = c) z = x+y 2xy x+y

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

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

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Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

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Q: Verify that 1 $(x, y, z) = satis fies the partial differential equation x² + y² +z? = 0 ax2 ay2 "…

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Q: Solve the following initial value problems using Laplace Transforms:

A: We need to solve the given differential equations using Laplace transformation. For (a),

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A: Let t be the time ,which is an independent variable (measured in days). We have to take two related…

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

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Q: dx 2х — dt dy – y = 6e3t, dt. dx 2 dt dy 3x + dt - 3y = 6e3t; %3D x(0) = 3, У (0) — 0. %3D

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Which of these gives an integrating factor for dy 2ty = 3t + 1 dt -

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Q: * = x- 2y+ 2z = -2x+y– 2z dt dy dt E = 2x – 2y+ z dt

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Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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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 dy -- x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: We will find out the required solution

Q: If x^2 + y^2 = 25 and dx/dt = -2, then what is dy/dt when x =3 and y = -4

A: Given that  x2 + y2 = 25   .... (1) dx/dt = - 2 To find dy/dt when x =3, y = - 4

Q: Find y". 25. y = x/2 - 5x 26. y = x2/3 + 4x 28. y = (x* + x)2/3 30. y = 2x5/4 + x!/2 27. y = (x³ –…

A: The given function is y=x32-5x

Q: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?

A: Given:

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

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Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: If y=x² - 4x and x = √2r²+1; find dy dt when t = √2.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: 5. dt3 d³x(t) 8 d²x(t) dx(t) - - dt + x(t) = u(t) 14 dt2 d²x(0) 1, dx(0) x(0) = 1 -2, dt2 dt

A: Given below the detailed solution

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: dx dy 2 + + x + 5y = 4t, dt dt dx dy + 2x + 2y = 2, dt dt x(0) = 3, y(0) = -4. +

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Q: dx If x2+y2+z2 = 9, dt dy = 6, find dz when (x, y, z) = (2,2,1). dt 4, dt dz dt when (x, y, z) =…

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Q: 6. If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: The given equation are x=y3-y,dydt=5  and y=2.

Q: Find the second order partial derivatives of S(r. y) = (3r +2y) Sm(r, y) = 36(3r + 2y)? Sw (r, y) =…

A: The given two-variable function is: f(x,y)=(3x+2y)4

Q: 1. Write down the system of differential equations for the gradient flow associated to V (x, y) : xy…

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Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: ,dz Find ifz = xy2 +x²y, y = ln x - dt

A: We are given : z=xy2+x2y and y=ln x⇒z=x(ln x)2+x2 ln x

Q: Find the integrating factor of (x^2−y^2−4y−5)dx+2x(x+y+2)dy=0

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Q: Solve y(1): dy/dt + x = 1; dx/dt-y + 4e¹ = 0; x(0)=0 and y(0)=0.

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Q: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

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Q: d?y 4- dt2 dy dy (-2) 9. + 28 + 49y = 0; ; y(-2) = 2 ; = dt dt 2 d?t dt + 9 dx dt (0) t(0) = 3; dx…

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Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

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Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

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Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

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Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

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