Find Laplace treins form for Ý +4Y+3Y = e y(o) =y co) = 1 %3D %3D

Q: Find Oz/ou and oz/ov for z=4e* ln(y), x=ln(u cos(v)), y = usin(v) at the point (u, v)=(2.7/4).

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Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: Determine the Integrating factor of the DE: y (2³e™y – 3) dæ + x (y+ x*e®v) dy = 0 -3 1

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Q: 1.5 (3-y Evaluate the integral dx dy using polar coordinate 'y

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Q: if y= e-e-X dy %3D Show that %3D e* te*

A: We have to prove this equation

Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? ... (2) ev²…

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Q: Sketch the x-y trace, x-z trace, and y-z trace. Determine the charge density of the electron cloud…

A: The complete solutions are geven below

Q: Use the Chain Rule to find dz/ds and dz/dt. z = x°y°, x = s cos(t), y = s sin(t) dz as az at %3D

A: Given:-z=x5y9x=scos⁡t,y=ssin⁡tTo find∂z∂s&∂z∂tBy chain rule∂z∂S=∂z∂x∂x∂s+∂z∂y∂y∂Swe…

Q: Determine the solution of the differential de +y cot x = cosx O a. ycos I : sin'z +e o b. ycos x =…

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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: y = In(sec t), x = log(cosec t) In(sect), x %3D %3D

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Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: Q2) A) Verify that Wxy Wyx for w = x sin y+ y sin x+ xy. B) Show that f(x, y) = e-2y cos 2x…

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Q: Find the two-term perturbation approximation to y" = e", y(0) = 0, (0) = 0. %3D

A: Given:                                    y"= e∈y                               y(0) = 0…

Q: The Bossel aquation of order one halt, f'y y -y-o, 10, + ty+ has two linearty independert selutiorm,…

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Q: dz Find given: dt z = zew, z = t°, y = - 5+5t dz Preview dt II

A: This problem can be solved as follows:

Q: The solution of Laplace equation d'u = 0, where 0 < x < 3 dx? and 0 < y < 2 with boundary conditions…

A: Step:-1 Since we know for Laplace equation if step size h= k then ui, j=14ui+1, j + ui-1, j + ui,…

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: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: y" + y = H (t – 3), y (0) = 0, y' (0) = 1 %3D

A: Formula used: 1. Lft-aHt-a=e-asFs2. Ly''=s2Lyt-sy0-y'03. Ly'=sLyt-y0 Consider the given initial…

Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? |

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Q: Determine the Integrating factor of the DE: y (x³e*y y) dx + x (y + x³e*y) dy 3 1

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Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Find au explicit solution for the IVP. (Show work.) dy y? = 2ty", y(0) = dt 4

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Q: Obtain the integrating factor of the non-exact DE, (2 + ycosx)dx + xcosxdy = 0. a. secx b. cosx c…

A: Integrating factor

Q: Find the integrating factor that converts the equation below into an exact equation y dr + (2x – y…

A: The differential equation of the form, M dx + N dy = 0 is said to be exact when…

Q: Find the work done in moving a point charge Q- - 20 1C from.the origin to (4,0,0) m in the ficld E-+…

A: To find - Find the work done in moving a point charge Q = -20 μC from the origin to 4, 0, 0m in the…

Q: 1. Find the total differential dw. x + y +z 3. w = xyz

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Q: Q2) A) Verify that wry wyx for w x sin y +y sin x + xy. %3D B) Show that f(x, y) = e-2y cos 2x…

A: A) given that w=x siny+ y sinx+xy               ...i show that- wxy=wyx differentiate equation (i)…

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

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Q: Find the total differential. w = e3Y cos(5x) + z5 dw

A: The total differential of a function w= f(x,y,z) with continuous first partial derivatives in a…

Q: dy 3. da + y = 2xy?e"

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Q: 3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions…

A: The Laplace equation is given by: r2∂2u∂r2+r∂u∂r+∂2u∂θ2=0 The boundary conditions are: ∂u∂θr,0=0,…

Q: Find the integrating factor that converts the equation below into an exact equation y de + (2x – y…

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Q: Usa el método de transformada de laplace  Y''+4y=cos x, sujeta a y(0) =1, y'(0)=1

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Q: Ex: verifay u = e* cos y is a solution of laplace eqution

A: Solution:Given             u=ex cos yTo verify u is a solution of Laplace equation:i.e.,…

Q: xy*-dy = (a* lIn a – y (а* In a - y %3D

A: we have to find the differential of ax=y

Q: 4) If a wire in the shape of the helix: x = 2 sin t,y = 2cos t,z = 3t;0 <t < 27, and the density is…

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Q: fi at nd laplace: {e}

A: Use the formula for the Laplace Transform for the given function.

Q: A- Use the separated solutions to solve the Laplace equation. in the region 00 given the boundary…

A: You asked two questions, that are not related. So by our guideline we can solve only first question…

Q: uct Theorem. 10. K y KM=

A: Solution

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…

Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣

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Q: Find Particular Sol. of  xsin2 ycosy y' + sin3y/ 1+lnx = 4 ; y(e)= π/2

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Q: the ( gmplicit valne ) Find differenciation of az at the given poin t. Sin (y)+ sin(yn) + Sin (z+X)…

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Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? (2) ey² (3) x²…

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