f(x,y) = x² + 3y² + +xy b. f(x,y) = /x² + y² a. %3D

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: The integrating factor of + 2.xy= 5x² is dx dy а. b. x2 e 2 C. 1 d. et

A:

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

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Q: i $ 6x³e**+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv = 3g(x)dx,…

A: Using integration by parts

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Sx + 2y = 0 xy = -2 (x, y) = ( (smaller x-value) (x, y) = (larger x-value)

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Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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Q: f(x, y, z) = xyz + xy3 + yz3 + zx3 %3D fy

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Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

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Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: VII. Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0 2.…

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Q: Find fzyx. 8.8 f(x, y, z) = x*y°z® +xy³ + y°z f zyz ||

A: GIVEN: f(x, y, z) = x4 y8 z8 + xy5 + y5 z

Q: 2-/2x+1 Let F(x,y) = C be the antiderivative of f(x) = What is the value of C if x=11 and y=20 ?…

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Q: An integrating factor of (xy? + 2x?y³) dx + (xy – x'y?) dy = 0 is

A: Given equation (xy2+2x2y3)dx +(x2y-x3y2)dy = 0or y(xy+2x2y2)dx + x(xy-x2y2)dy = 0 here  M…

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: 3zyz f(x, y, z) = e %3D fz fy = f =

A: The given function is f(x,y,z)=e-3xyz. Evaluate fx as follows. ' Thus, the value of fx is…

Q: Integrate the following using substitution 1) z5 (9z6 – 7)8 dz 2) S dy 4 y3 2-5y4

A: Given that: 1. ∫z5(9z6-7)8dz   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: otain the solution using Integrating Factors y(y+2x-2)dx - 2(x +y)dy = 0 %3D

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Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Find the integrating factor for dy – 2xy dx = x dx. А. e1-2у %3D C. e1+2y 1 В. 1-2у 1 D.- 1+2y

A: Given the differential equation

Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

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Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: fy = e*, y = 1 - e-x, and x = 0 ab- %3D

A: Given: - The curves of, y=e-x, y=1-e-x and x=0 about y=4.5 To find: - The volume of a solid is…

Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: (x + 2y - 1)? dx = dy A. x + Arctan { [V(2)] [(x + 2y -1)] } = c B. x = Arctan { [V(2)] [(x+2y-1)]}…

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Q: dx = -y+y(x² + y² dt dy = x – x(x² + y²) - dt

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Q: Find the integrating factor. c. ydx + (3x – xy + 2)dy = 0 d. (x² + y² + x)dx + xydy = 0 (3x -…

A: A differential equation is in the form M(x,y)dx + N(x,y)dy = 0 and if it is not exact Then we can…

Q: II (2x + 3y + 4:") dV , where B = {(x, y, 2) | 0 < x < 1, 0 <y< 2, 0< 2< 3}

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Q: Find fy and fy: f(x,y) = - 3 e 4x-5y f,(x,y) = D

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Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: f (x, y) = 4xy² + 5a°y fzy (1, 1) = hx

A: Given: - The function is, f(x,y)=4xy2+5x3y To find: - The value of fxy(1,1)=

Q: dy + ydx %3D = 3x²y?dx,

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Q: valuate dy and A v for v = f(y) = x2 -6x +35 x =4 and dy = Ax= 05

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Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: O fi[0,00)→R all continious Aunction aro Sx³f(x') dx = Sx f(x) abx %3D show this.

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Q: sec y Then y8 Let z dz dy y16

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Q: An integrating factor of (xy? – x?) dx + (3x?y² + x?y – 2x³ + y?)dy = 0 is A) ey B) ебу 1 C) 6y e D)…

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Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration