1-r-y C * (r* + y° +:')}dzdydx 14

Q: 2. y(3x* + x°y$)dx – 2x°dy = 0 (use integrable combination only) -

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Q: Obtain the DE based on given conditions solve for item 1 only.

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

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Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

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Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: lim Y+ Y Cos y Yo 4 Siny cosy

A: Given limy→0y+ycosy4sinycosy

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: 1. 3(3x2 + y²)dx – 2xydy = 0

A: According to our guidelines we can solve only the first question. Please re post the other questions…

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = tanh (x + 2y + 3z)

A: We have given fx,y,z=tanhx+2y+3z and we have to calculate fx,fy and fz

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 3(1 + 2) - dy 2ty(y – 1) dt

A: The method to find the solution of the differential equation helps to find the required solution.…

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

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Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: lim (z,y) (1,1) 2x – ry – y 22 – y?

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sinh (xy - z2)

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Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

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Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

Q: 1 J sec- ztan - zdz

A: Solve the following

Q: 2-g(%,y)%3D플-플 * at (VT ,1)

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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: = (u² - cos v, u + sint, cos v) x(u, v):

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Q: 3. f sin³y(2-3cosy)² dy

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Q: Intergrate dy (2y-x) =In Co)

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Q: 2dy -2y 2. zt at

A: Solved below

Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: 5. y" – 2y' + y = 2sinx cosx y'(0) = 0,y(0) = 0 %3D | -

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Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

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Q: Sin'z dz 4.

A: Note :- These are multiple questions and you not mention here whose solution you want. So i am…

Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

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