1. Verify that the Laplace's equation: (i) u =x+3xy² (ii) u = sinxcoshy+cos.xsinh y f the uove equation

Q: Show that f(x, y) = e«" (A cos(ay) + B sin(ay)) satisfies Laplace's equation: = 0.

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Q: Find the differential of each fuction. a) %3D dy= ? b) U COS U dy= ?

A: Given,  (a) y = s7+8s  (b) y = u cosu  We have to find the differential of each function.

Q: When is the derivative dy/dx of the parametric equations x(t)= 3cos t and y(t)=3sin t for Ost22n…

A: Let's find.

Q: Solve using Laplace Transforms y"+4y = t-2 sin t; y(0)=-1, y'(0)= 2,

A: given differential equation isy"+4y=t-2sinty(0)=-1y'(0)=2applying laplace transformLy"+4y=Lt-2 sin…

Q: Show that z=tan-1(2xy/x^2-y^2) satisfies the Laplace equation

A: The given equation is, z=tan-1(2xyx2-y2). Obtain the partial derivative of z with respect to x as…

Q: þ/ Show that the function satisfy Laplace equation f(x,y) = In /9xy+3y²

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Q: 4. y = c, sin wt + c, cos wt w is a parameter

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Q: Write the differential dw in terms of the differentials of the independent variables. w = f(x,y,z) =…

A: Hair we have to find out the differentials

Q: 1. Given r(t) = 2 cos t i + 2 sintj+ 10tk; 0 <t< 2n , find the tangential and normal components of…

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Q: Show that the function f(x,y)=ln√x2+y2satistes the Laplace equation.

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Q: þ/ Show that the function satisfy Laplace equation f(x,y) = In /9xy+3y² Q/ find by using chain rule…

A: Since you have posted multiple questions ,we solved the one question for you  To get the solution of…

Q: Consider the graph of f(x, y) = excos(xy²). Find an equation of its tangent plane at (0,0, 1) and…

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Q: 10. Does the function f (x, y, z) = (x² + y2 + z?)-1/2 satisfy Laplace equation?

A: The objective is to check the given function satisfies Laplace equation or not.

Q: solve this initival value question using laplace tranformations: y''+4y=(t^2)δ(t-4), y(0) = 0,…

A: The given IVP is           y''+4y=(t^2)δ(t-4), y(0) = 0, y'(0) =1

Q: Solve this equation by using laplace  y''+2y'+5y=e-tsin(t)   y(0)=0, y'(0)=1

A: In this question given that a differential equation and we find solutions of this by  using Laplace…

Q: 11. Find an equation of the tangent plane to the surface T+VG+vz = 4 at the point P(4, 1,1).

A: we have to find the tangent plane on the given surface x+y+z=4 at the point P(4, 1, 1)

Q: Show that the function z = 1/2 (ey − e−y)sin x satisfies Laplace’s equation          ∂2z / ∂x2 + ∂2z…

A: Given that, z=12ey-e-ysinx

Q: 3-) The following f (z) function 34 e 18 1Z +22, (7) J Sint t> 2, find the Laplace そronserm.

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Q: The function u(x, y) = 2020xY is a solution of the Laplace's equation True False

A: The given equation is: ux,y=2020xy  The given function is a solution to Laplace's equation.

Q: find the decomposition of a(t) into tangential and normal components at the point indicated r(t) =…

A: The given vector  rt=t,cost,sint ,      t=π2 To finding the components of acceleration take the…

Q: Solve te following DE using laplace trancform - 3X ty =e cos2x when ylo) = 0 %1

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Q: Determine whether the given function satisfies a Laplace equation. f(x, y) = e 9Ysin 9x No Yes

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Q: Show that the function z = e* sin y satisfies Laplace's equation a²z a?z = 0 дх? ду?

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Q: Show that the function f(x, y, z) = x² + y² – 222 sat isfies the Laplace equation. - Good Luck.

A: Given function f(x,y,z)=x2+y2-2z2. We have to show function satisfies the Laplace equation. A…

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: show that the Punctionc Sinh t V3 and ye T5 Sinh t+ CoshE 13 taken together satisfy thediff erential…

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Q: Show that the following function satisfies the two-dimensional Laplace's equation. z = In(x² + y?) +…

A: Solution:Givenz=ln (x2+y2)+2 tan-1 yxFormula:ddxln x=1xddxtan-1x=11+x2ddx(xn)=nxn-1To prove:z…

Q: 19. Solve y'(1) + y(t) = sin t; y(0) = 1 by Laplace transfrom. %3D

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

A: Formula Used:L{y''}=s2Y(s)-sy(0)-y'(0)L{y'}=sY(s)-y(0)L{eat}=1s-aL{tneat}=n!(s-a)n+1

Q: Show that the function f(x, y) = e-2y cos 2.r satisfies the Laplace equation.

A: use partial derivative to check whether it  satisfy the equation or not

Q: Solve

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Q: Show that the function f(x, y, z) = x² + y? – 2z² satisfies the Laplace equation.

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Q: Show that the function satisfies the Laplace equation f (x, y, z) = (/x2 – 2y² + z?)*

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Q: S how that f (x, y)= tan! Satio fy the Laplace equation fae + fyy =0.

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Q: Consider the 2nd order equation 2²y+ Sin dy y² +y = Choose the ight assertion A) the linearized…

A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

Q: Show that the function f(x; y; z) = 2z3- 3(x2+y2)z  satisfies the Laplace equation.

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Q: Q3) For the following function: 1 U= zlog(x² + y²) 1. Determine whether it is harmonic (satisfy…

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Q: y"+2+y=e^5t y(0)=0 У (0)-5

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Q: a²z + ax? (c) Show that the function z = e* sin y + e cos x satisfies Laplace equation a²z = 0. ду?

A: Since you have posted multiple questions in this question which are not interlinked so I do first…

Q: Show that if the function f(x, y) = ecos-e-cosx, satisfies Laplace Equation.

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Q: (c) Show that the function z = e* sin y + ev cos x satisfies Laplace equation ax? a2z = 0.

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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: use laplace truns form to Solve Y't Y = f(t), y (0) = 0, where

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Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: It is given that,xey+sinxy+y-ln2=0.We have to find the value of dydx at the point 0,ln2.

Q: E. Show that the function e sin y equation satisfies Laplace's a²z a²z 0.

A: E) z=exSiny.

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

A: We have to verify that the equations satisfy the given conditions.

Q: Show that the function z = ex sin y satisfies Laplace’s equation                      ∂2z / ∂x2 +…

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Q: Ex. 5. Find a solution of Laplace's equation, u +u, =0, inside a rectangle subject to the following…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: how that the function satisfy Laplace equation f(x,y) = In /9xy+3y²

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