1. Given the Lagrangian L = xỳ +2xyx + x²ì − x³, - ⚫ find the constants of motion,

Q: 4. Solve the Poisson equation, V2u = e²y sin x 0<x<π,0< y <L subject to the boundary conditions,…

A: Here, we can use the method of separation of variables. However, the boundary conditions are not…

Q: Find a formula for the average velocity, vav(t), on the time interval [t, 7] for t n. Vav (t) Find…

A: An object moving in a straight line with a displacement function s(t), then its avg velocity between…

Q: 5. (a) Evaluate the line integral % 2 dic + dy+yz along the curve C(t) = [t², t³, t²], ɩ € [0, 1].

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Q: 5. Let W R³ be the intersection of the two planes: 2x + y − z = 0 and 3x - y + 2 = 0. Find the…

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Q: 1. In this problem you will prove that the shortest distance between two points is a line using the…

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Q: 2. Consider the spherical coordinate system Z X 0 * (r, 0, 0) 11 I y a) Express x, y and z as…

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

Q: Problem 6: In class, we showed that at an arbitrary point P with spherical coordinates (r, 0, 0),…

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Q: Find the general solution to the differential equation y" = 2– sin 2r.

A: y'''=2-sin2x

Q: 3. Consider the following matrix: [1 2 21 A = 2 1 2 L2 2 11 (a) Determine the eigenvalues and the…

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Q: Suppose that, while lying on a beach near the equator of a far-off planet watching the sun set over…

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Q: Find the arc length parameter along the given curve from the point where t= 0 by evaluating the…

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Q: Evaluate the integral from -∞ to ∞ of the expression exp ip²t 2mħ 4ah² + ipad + fact that the…

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Q: Suppose that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?

A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ

Q: In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" + by'…

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Q: find u(x,y) , v(x,y) where f(z)=u+iv for function f(z)=Z2 e2z

A: Given, A complex function fz=z2e2z