Sketch the x-y trace, x-z trace, and y-z trace. Determine the charge density of the electron cloud if given p(x, y, z) = xyz %3D m3'

Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t = 0 1 1 1 T(0) = V3'…

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Q: r q'(r,z) = q%kJo] 2.4048- TCZ cos L. ER

A: Given We can partially differntiate with respect to r and z as shown below.

Q: 2. g'-yso ylo)=2 gilo): -2 y'Co)= y'(0)= -2 : -2

A: Given: y''-y=0, y0=2, y'0=-2 So, we can also write as: D2-1y=0   The auxiliary equation is: m2-1=0

Q: se-* 0<x< c0 Q4/ Let X,,X, and X, be iid with common pdf f(x) = { e.w and let Y, X Y2 X2 Y, = E- x…

A: Use the additive property of independent exponential variates and the ratio of dependent gamma…

Q: A. Solve the differential equation B. Find the moment of inertia ly of the region bounded by the…

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Q: Find the solution of the following Differential Equations .by Exact 4) 2.xIn(y)dx+ y'x'dy 0

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Q: Question 4 If z fx, - Ax, y) = x* - xy – y°, find the differential dz OA dz = (2x - y)dx + (-x –…

A: Given: z=f(x,y)=x2-xy-y2Then,dz=∂z∂xdx+∂z∂ydy

Q: Find the integral durtace of the partial dlifferential eggaation

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Q: Show that the Euler-Lagrange equation for the functional 1 S[y] : + y² + 2xy)dx, y(0) = 0, y(1) = a,…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t=0 T(0) = N(0)

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Q: Let a <b, A and B be constants. Find the Gâteaux differential of the functional ·b 2 S[y] = ["* dx…

A: I have written the solution in Latex.

Q: If the D.E. y dæ + N(x, y) dy = 0 is not exact and OM _ ON = -1, then the integrating factor is u =…

A: If the DE ydx+N(x,y)dy=0 is notexact and ∂m∂y=∂N∂x=-1 thn theintegrating factor is m

Q: Evaluate the following integrals, the contour Cbeing taken in counter-cbckwise sense sin'z (a)…

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Q: Exercise (1): Determine the order and degree of the following differential equa- tions: (1) y - 4x +…

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Q: of Find and for the following function. f(x.y) = e 6xY In (5y)

A: The given function is: To find the partial derivative:

Q: 27" + 4y = t Yo) =1, y'c0) = 2 %3D %3D

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Q: Question 6 8(x,z) = 2xz+3z-x X-Z Let f(x,z)= Z. 2z2–3 Blank 1: Find the total differential of f(x,z)…

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Q: If Z = Jxy +y, x= cos 0 , y= sin 0 when 0 dz By using chain rule find de

A: Chain rule for one independent variable- Suppose that x = g(t) and y = h(t) are differentiable…

Q: dy = f'(x)dx: 1. y = In (1+x²) %3D

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

Q: .il ll.רמNs 16 9:15 PM • A57 1-i-iv- Find extr... Find extremals of : i) J(y) = | (e' +xy ')dx. y…

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Q: ii) J(y)=[(e" *y")dx, y (0) 0,y'(0) =1,y (1) =e, y'(1) = 2e

A: Solution 2: Given functional is J(y)=∫01e-xy''dx, y0=0, y'0=1, y1=e, y'1=2e. To find the extremal of…

Q: vi) J(y) = [(y," -y)dx ext, y,(0) = 2, y,(1) = 0, y (0) = 0, y,() 1, y, (0) 1, y,(1)=0

A: Solution 6: Given functional is J(y)=∫01y1'2-y2''2dx, y10=2, y11=0, y20=0,  y21=1,  y2'0=1,  y2'1=0…

Q: b) Find the potential P(x,y) attached to the exact ODE 2x sin(y) + x² cos(y) y' = 0 %3D

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Q: Let a < b, A and B be constants. Gâteaux differential of the functional ·b [* dx (y² +w²y² + 2yx¹),…

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Q: For spring-mass model x" + ' + x = cos(wt), find the practical resonance frequency, and the steady…

A: For the spring mass model  mx''+bx'+kx=Fcosωtsteady periodic amplitude is given…