let be Solve 1G:= {(x, y) ЄR² = (0,2), y = (0, 2)}" Ω:= = {(x, y, z) = R³ : x = (0, 2), y Є (0,2), z Є (0, 1)} = G × (0, 1) . du(x, y, z) = 0 (Au(x, y, z) = 0 V(x,y,z) ΕΩ V(x, y) Є OG x (0, 1) (x, y, 0) = 0 V(x, y) Є G ди მა (x, y, 1) = cos (πx) + cos (лy) +7 cos (2πx) cos (TV) V(x, y) = G.

Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: If U(x,y)=In(x²-y³) then Ux+Uy= ... XX

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Q: Solve Fyy + 3 Fxy + 2 Fxx 3D х, F (х, 0) 3D —2 х,д, F(х,0) — 0. ху XX F(x, y) =

A: To solve the below partial differential equation. Fyy+3Fxy+2Fxx=x,  Fx,0=−2x, ∂yFx,0=0

Q: If y=x*, then y' (1) = A) 6 B) 12 C) e6+12 D) In(6) + 1

A: Given; if y = x6x , then y'(1)=?

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: The equations cos(u) + 10uy2 + e + 2 = 0 and 2ye" + 4x2v - 3xcos(z) +1 =0 are solved for u and v as…

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Q: Suppose z = x² sin y, x = -4s² + t², y = -2st. A. Use the chain rule to find and as functions of x,…

A: Given:The functions .To find:The values of:a) b) The numerical values of  at .Concept Used:Power…

Q: 2 4 Ayz x = By + Cz' ||

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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: la - b| si a = -1 yb = 8 → -9 -7 7 >

A: According to our rule we can answer only first question. Use the concept that negative quantity…

Q: If y=t3, then y(6)+y(5)+y(4)+(1/3)y'=y? What is the power of y? a) 0 b) 2/3 c) 1/3 d) 3 e) 2

A: Differentiation of y with respect to t can be given as:

Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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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: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: 2) a) Let T: C² C²: Ty = [x+2y-iz] 2y + iz Lix+z-2z Find [7] B [7] B and P where

A: Given information  T  :  C2 →C2T xyz = x+2y-iz2y+izix+z-2z simplify it, T xyz = x+2y-iz2y+izix+z-2z…

Q: 2x (x-6) 3.) y = (x-3)3 required:a) yand y"

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Q: Resolve xy +y = e", y(1)= 2 a) y =+2+e* b) y = c) y =+2- d) y = +2. a- e* +2-e e) y =

A: Given that  xy'+y=e^x  To solve the differential equation

Q: Solve for x, y z from X - 1 1 2 Z 3. 6 6

A: 2x-113y=2z66

Q: Suppose z = x² sin y, x = -4s² + t², y = -2st. A. Use the chain rule to find and Əs Ət = as…

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Q: 2 a) Solve x y'= (2+ yx)·

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Q: bj f(x,y)= еху cЈ fexiy>= x cosx cобу p² d.j fexiys= (x'y 2) log (x'ty ?).

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Q: 2. Let AX = B with 2 1 1 3 ^= [₁ ²²² =²×²0 EJ A: 0 -3 -2 B X y ) 2 1 use the fact that 1 A-¹ = 2 -3…

A: We have to find the value of variable and verify them the result

Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: The equations xcos(u) + luy² + e² + 2 = 0 and 9ye" + 4x²v – 3xcos(z) +1=0 are solved for u and v as…

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Q: The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x,…

A: Consider the given information. utt=uxx                 -∞<x<∞t>0ux,0=2xutx,0=e-x D…