dy If ex+У%3D ху, then dx %3D Ух- 1) A x(у- 1) (1- x) B x(y- 1) x(у- 1) Ух- 1) x(1-у) (D y(x- 1)

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: dy If 3x -1 and if y= - 1 when X=1, then y= dx A x³ - x-1 x³ +1 © x³ - x+1 D -x3 + x-1

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Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7. fxy(x,y)=

A: Concept: Partial derivatives: In differential geometry and vector calculus, the partial derivative…

Q: 8-2² y² dzdx dy x+3y 3-3X 3-3X-y dzdyd% SS(x+y+z)dy dx dz

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Q: (2x-3y)dx+(2y-3x)dy3D0

A: As per our guideline we are allowed to answer only one question. Kimdly repost the other question as…

Q: fx=å (3in (x*ry)-x2) %3D fy = Ly(31n (x*+y)-x2) %3D d fe-(3in (x*ry)-x2)

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Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: 6. (2z – 1)(y – 1)dr + (x+ 2)(x – 3)dy = 0, y(1) = -1

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Q: (3メーy-4) dy (x+y-4)dx when x« 3, y=7

A: As per our guidelines we are supposed to answer only one. Kindly repost others question as a…

Q: 2. (2x + 4y -3) dy + (x + 2y -1) dx = 0; y(2) = 5. Determine y(3)

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Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral

Q: Find fxy(x,y) if f(x,y) = (x5+y³) 7. fxy(x,y) =

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Q: 1. (2x6x5 +7x³-3x² - 11) dx 2. f(9y2 +6y-4-y-5+1) dy (12x-x+x) dx 3.

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Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: Given: f(x,y)=ln|3x4+5x2y2|∂f∂x|(2,−1)=fx(2,−1)=?∂f∂y|(−4,3)=fy(−4,3)=?

Q: 2y (x+y+2) dx + (y²-x²-4x-1)dy = 0 when x=2, y= 3 |

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Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7,-5)

A: The given integral is ∫C2x-y dx+x+5y dy where C is the line from 0,0 to  0,-5 and  0,-5 to 7,-5. To…

Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: V2x-x2 SS2*-*" (x² + y²) dydx

A: Changing cartesian to polar coordinates: x2+y2=r2x=rcos θy= rsin θ x ranges from 0 to 2y ranges from…

Q: 2) (-4у + e-3*)dx %3D 4 dy

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Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

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Q: Find the function y(x) satisfying -8/9 = 6x dx and y(-1) = - 4. dy :-8/9 The function y(x)…

A: Integrate the equation dydx=6x-8/9 with respect to x.…

Q: 2. (2x+4y-3) dy + (x+2y-1) dx = 0; y(2) = 5. Determine y(3).

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Q: 1. y = - V2x +1 2. y = (x – 1)3 + 2 3. y =-1 2x

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (2,5, – 6) | 16x dx + 4y dy + 2z dz (0,0,0)

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Q: (6x -3y +2)dx - (2x– y – 1)dy = 0 (coefficients linear in two variables)

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Q: 4. (-3x + 2y) dy + (-3y + 2x) dx = 0; y(3)=8. Determine y(5).

A: Given that -3x+2ydy+-3y+2xdx = 0 where y3 = 8. The objective of the problem is to determine y5. We…

Q: 3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

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Q: dx + 6x = 3yæ y- dy 1 1 x = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 y = (x + x²C)³ x = (y +…

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Q: xydy - y^2dx = x * [(x^2 - y^2)^0.5]dx

A: First order non linear differential equation. Given differential equation is homogeneous, for…

Q: (2x-3y+6)dx-(4x-6y+2)dy=0 in Linear two variables with POI

A: Here, the given differential equation is: (2x-3y+6)dx-(4x-6y+2)dy=0 The equation can be written as:…

Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

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Q: dy 6-x.-3y= x' dx

A: we are given an ode -x*dy/dx -3y=x2 we have to solve this ode as we can see, this is a linear first…

Q: (3x°y+2e2y + 3)dx + (x³ + 4xe2y – sech² y+2ln y¯)dy = 0

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Q: 14-2x 1. ! ] dydx 0 2 2. dxdy 0 y 11-r 3. dycx o 1-x 4. [[ dydx 0 0

A: Answer 1: changing dy dx to dx dy; limits of integration: 0 ≤ x ≤  [2 - (y/2)] 2 ≤ y ≤ 4

Q: Evaluate / (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7, -5)

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Q: (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

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Q: dy 2 = 3, ,3 X'y' - xy dx

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Q: 3z (sec-(-3z?))³ 2|–3z*|-/9zª–1 If y= sec-1 (-3x²), then dy dz

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Q: 2x-3y+6)dx-(4x-6y+2)dy=0

A: Given that: (2x-3y+6)dx-(4x-6y+2)dy=0

Q: (2x - xy - 2y+ 3)dx – (x²y + 2.x)dy = 0 when x= 2, y =-3 %3D |

A: Ordinary Differential Equation: When an equation contains derivatives with respect to a single…

Q: dy_2y-x+5 dx 2x- y-4

A: Find the solution of the ordinary differential equationdydx=2y-x+52x-y-4

Q: min f (x, y) %3D (х - 4)2 + (у — 4)2 subject to х+y<4 and x+ 3y <9

A: Given that x-42+y-42 subject to x+y≤4 and x+3y≤9. The objective is to find the maximum through FOC…

Q: dx + 6x y- dy 1 y = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 (y+ y²C)³ (x + x²C)³ Option 3 Option…

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Q: f (x, y) x+ 3 ху 3 Бъ-х

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Q: 3 2 | z=1 y=1 -2(x + 1)y dy dz بائية

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Q: dy 3e-2x %3D dx 3. (x2 + 5)dх — (2у — 1)dу %3D0 (2у — 1)dy 30 |

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Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

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Q: Find f, (X,y) and fy(x,y). Then, find fx(-3,1) and fy(-4, - 2). f(x,y) = - 2xy + 3y + 8

A: Given that: f(x, y)=-2xy+3y3+8

Q: 2 - (2x 3y)dx - (2y + 3x)dy 0

A: 2)-(2x-3y) dx-(2y+3x) dy=0dydx=(2x-3y)-(2y+3x)dydx=3y-2x2y+3xdydx=3yx-22yx+3y=vxdydx=v+xdvdx