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Q: Suppose w = In(x² + y² + z²) , x = ue³" sin(9v) , y = ue3" cos(9v), and z = ued". %3D Compute dw/du…

A: If w is a function of three variables, such that w(x,y,z) and x, y and z are further function of u…

Q: Find y' at the point (7, 7) where z sin(z? – y*) + 46 = z² – 3. Türkçe: z sin(z² – y²) + 46 = z² – 3…

A: To find y' at (7, 7) Where  x*sin(x2 - y2) + 46 = x2 - 3....(1)

Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

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Q: Evaluate the line integral / (x+ 2- rom (0,0) to (3, 0), the path C2 fro co (0,0) by applying the…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: 5) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a…

A: We have to find out the potential difference at various points.

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: Evaluate the spherical coordinate integral. 1- cos 2 2x x SS S p²sin dp do de 00 1- cos 2 2x x SS S…

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Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

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Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: nclude spaces in between 5. d te In (In y)) at y dy

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Q: Use Green's Theorem to evaluate the integral (y - x)dx + (2x - y)dy for the given path. C: x = 2…

A: Definition used -                                According to the green theorem -…

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many…

A: Consider the given path rt = cost , cos2t , sint  Then, xt=cost , yt=cos2t , zt=sint

Q: Show that the spherical harmonics 1 3 sin 0 e-iº, 2V 27 Y1,+1 and 3 1 Y1,0 2V V cos 0, %3D | are…

A: Given: The given harmonics are Y1,+1=1232πsinθ e-iϕ and Y1,0=123πcosθ  are orthogonal over the…

Q: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

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Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

Q: f(x, y) =(e-2y)Cos2x

A: The Laplace equation is: ∂2f∂x2+∂2f∂y2=0

Q: Consider the cune C: (x-8)+ 4-7) When parametneing C, A tungent veotoar is i O a) r (0) = (8 +3…

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Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

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Q: (a) Suppose that a black hole has magnetic field F = (2a* + e" sin(2), y³ + xe*, 2z³ + e" cos(z) +…

A: TO FIND: Magnetic flux across the black hole

Q: show that fGx) = C,ex +C,e* s a solution to y for all real conatanto C, +C2, and then find C,, C,…

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Q: 1 use that transformations e Jaco Je √y=0 p√x=0 %cty octy=u dy dx = e = 1 2 and your to prove

A: An equation is given by, ∫x=01∫y=01-xeyx+ydydx = e-12. The objective is to use the transformations…

Q: If F(x, y) = (6xy - 1,3x2 + 2y) and C is the circular arc along x² + y? = 2 from (1, 1) to (-1, 1),…

A: Given vector field is  F(x,y)=6xy-1,3x2+2yF(x,y)=(6xy-1)i+(3x2+2y)j c is the circular arc along…

Q: Qs Findl the Fauier Ex pensian of Hhe funckian deld in a gula Parul by the weladons Sule Perial by…

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Q: (b) f(u) = tan(arccos u). FRAS SER UNIVE ERS %3D ERSI TY OF fficial que s test question question ion

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: of the b) nd y- Fons c) with point.

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Q: So lve the se cond order boundary Valye eF problem: Y+y+2yso where y (0) = || and y'lo)s 18

A: The given differential equation is y''+y'+2y=0......(1) with boundary conditions y0=11 and y'0=18…

Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: 8. Set S be the bondary of the cube with side length 1 in Oc tant 1. Is in 6 pieces) Use Stokes…

A: (1) Over the surface ABCD ∫sx dy dz +z dz dx=∫01dz∫01xdy…

Q: iven that use the bhi tzS to compute %3D irst shifting Theorem [e"e cos 7+]

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Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…

A: FORMULA USED- For  f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: eiz dz around (a) |z – in| = 2 (b)|z - | = 2 (c)|z| = 2 sinhz

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Q: 13-Evaluate JJI zdV E where E lies between the spheres x2 + y? + z2 = 1and x2 + y? + z? = 4 in the…

A: The given integration is , Let, I=∫∫∫EzdV change the integral into spherical coordinates Put x=r…

Q: 7. Prove that the SolutmM of y + y = o is B sinx (hint y= Xu) by using Bessel's Functron definstian…

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Q: ) Use the eisenfunctan expausian melbud Solve the vibrating strng Problem = 4 uxx + Sin zx…

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Q: Eveluake F.dv wlere flaiy,z) where the segnent on Cis (-',2,0) to (3,0,1)

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Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·

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Q: (z+1)dz Evaluate using Cauchy's Integrati on Fromula where Cis z+2| z'4z

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Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

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Q: find the valume 9tntrat ed by y= X? on [0,31 rotating abaut thlina X-5.(shell melthod) rated

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Q: D.Prove that y y(2)= U12,9)+ jve (2,4) anelyli the loplale's as z, than Guetion u and v Satiglics

A: Consider an analytic function f(z) of the form . Then f(z) will satisfy the Cauchy-Reimann equation…

Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…

Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: Prove that the integral: √ [2xyz² dx + (x²z² + z cos yz)dy + (2x²yz + y cos yz)dz ] Is independent…

A: The given integral is ∫C2xyz2dx+x2z2+zcos yzdy+2x2yz+y cos yzdz. The objective is to prove that the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.