Problem #2: Let A Problem #2: Let B 8(u, v) = Find C g(u, v) Problem #2: Let a²g(u, v) dudv Findg(u, v) Find Su + 6v uv² 9u+7v U″Y g(u, v) = at the point (u, v) =(4,-4). at the point (u, v) (-5,-4). 5u + 6v uv² a² g(u, v) dudv at the point (u, v) =(4,-4).

Q: a) Which of the following systems of ODES is autonomous and dynamical? where ty₁ = e-sin(₂), y₂ = ₁…

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Q: estimate parameters and draw CRD model.

A: let us take the given linear model  Yij=μ+αi+∈ij where i=1,2,3; j=1,2

Q: 8. Reflect triangle LMN with vertices L(-2, 3), M(1, 4), and N(2, 1) over the y-axis. 4y L'= M' = N=

A: Given is the triangle with the vertices L(-2,3), M(1,4), N(2,1). It is needed to transform the…

Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

Q: 2. (Section 17.7) Verify Stokes' Theorem for F(x, y, z) = if C is the intersection of z = 4+ y and…

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Q: If u = x²/(x² + y²), find ou/ox, du/dy.

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: y = [ 0 1] (2x2 matrix) + [-1 0] d/dx y [1] (1x2 matrix) y (0) [1] [1] %3D [2]

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Q: 12.) Let h: IR³ -> IR5 and g: IR² -> IR³ be IR² -> IR³ be given by hcxy. 2) - (xyz, ex* x sin(y),…

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Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

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Q: (Section 17.2) Find the total charge on a wire in the shape of curve C: x² + y² = 4 in the first…

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Q: 2. Solve V'u = 0 for r<1, 0<z< T, u(r, 0, 0) = 0, a7(r, 0, 7) = 0, - u(1, 0, z) = z cos³ 0.

A: It is given that

Q: 10) *- dy + 8, y(1) = 1 10) dx A) y = Vx + 8x - 8 В) у%3D 1 + 8x - 8 27 C) y =x + 8x + 10 D) y = +…

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Q: У ,ーテ = ,-, + テ-テ - y = y: ij ij i. i. and (y;-y 10, – 7,) + 6, - 7) | ij ij i. ーリ-bー)+G.-) 2 2 2…

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Q: Verify that the vector X is a solution of the given homogeneous system. -1 x-(-; X'= 1 -1 x - (-²)…

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Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: 1. R= {(1, 1), (2, 2), (3, 4), (5,9)} C ZX Z 2. R= {(n, m) ENXZ: n² = m} CNXZ 3. R = {(n, m)…

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Q: 3. If z* +x²z+z+y = 0 find (1) Əz/ax, (2) əz/əy, (3) ²z/dx², (4) d²z/@y², (5) Fz/dxəy, and (6)…

A: As per our guidelines, I am only solving the first three. For other kindly upload the question…

Q: 4) Solve via separation of variables: u(0, y) =0 ди -(2, y) = 3sin a'u a'u +5 sin =0 ; 6. S0<x<2…

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Q: 1. Disk Method a. y = x2,x = 0, x = 2, y = 0, about the x ахis а.

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Q: Suppose a mechanical oscillator obeys the IVP y" + 4y' + 5y = 0 y(0) = 0, y'(0) = 1 (1) Note: Write…

A: Given  yy''+4y'+5y=0, y(0)=0, y'(0)=1

Q: ut = 2uxx осхез ux (0₁ t) = Ux (3₁ t) = 0 cos. U (x, 0) = 4, COS 2 TX - 2 cas y mx TT t>o

A: As multiple questions are there and it is not mentioned that which question to be solved, I will…

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Q: 12 2 5[1₁ Y>] = {dx [74, ² + 24 y/y + z\y 2² +4y² ² + 12yy₁ + 99² ² ] Euler - Lagrange equations for…

A: To find the Euler-Lagrange equations for the given Lagrangian L, we need to calculate the partial…

Q: Find the equations of the reflection in the line y=x+1. a) x' = y - 1 , y' = x + 1 b) x' = x - 1 ,…

A: Given: Equations of the reflection in the line : y = x + 1

Q: The equations re + uz – cos(v) – 2 = 0 and u cos(y) + 4r?v – 5yz2 – 1 = 0 can be solved for (u,v) as…

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Q: 2) Discuss the type , linearty, singulavity and homugenity d- the following equations; )) ux)=1-x+…

A: Given: (1) u'(x)=1-x+∫0xu2(t)(x-t)3dt, u(0)=2 (2) u(x)-1=∫0xcot(u(t))dt-∫-11(x-t)2u(t)dt (3)…

Q: Əz Əz Əz 2. Find where Ju' Iv' I w z = x² + xy³, x = uv² + w³, y = u+ve".

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Q: 1. R_(C,α) (x,y)=(−y,x) is a rotation about the origin C = (0, 0) by some angle α.  Find the angle…

A: Let's find.

Q: - (y-2u) + u, y = -2 x- y, u(x, 1) = e. find an explicit solution for u = u(x, y) sub

A: Introduction: A partial differential equation is known as Lagrange's type if it is of the form…

Q: The goal of this problem is to fit a trigonometric function of the form f(t) = a sin(t) + b to the…

A: Given,       f(t)=asin(t)+b, to the data points 0, -6, π2, -7, π, -7, 3π2, 3.

Q: Q2)A) If U (x,y)%3DXY-sin n is a function and x,y are function of r,9 defined as follow x =r cos 9 y…

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Q: 2y )dx - (x +3 cos y)dy around the parallelogram havi - 6

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Q: Q11) Let T₁ = 0, 7₂ = 3 be the roots of the indicial equation at x = 0 of the D.E. xy" - 2y + y = 0.…

A: Given D.E and indicated equation has different roots and  is the solution corresponding to

Q: If I(x) = | u"-1e-" du, therefore 0, r°(x) = (u*)*-e" du du -u? 0, O Option 1 r°(=) = (u")** e " du…

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Q: , Which of the following processes is stationary? A) An MA(1) process with 0 = -1.6 B) Y, = 58.46 +…

A: The stationary process is