Show that 2x9 2. by laplace. Egivahin fax+ fy =0

Q: Determine L{5 – 3t + 4sin2t – 6e"} by using the Laplace table

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Q: Let, T: R' → R';T(x, y,z)= (x+y + z,2y + z,2y + 3z Tost uhothor the troncfCormotion T is linoer

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

A: Solution:Given   z=ln (x2+y2)+2 tan-1yxTo prove :∂2z∂x2+∂2z∂y2=0Formula:∂∂xln…

Q: Qr what is laplace tHansfermatun bun T= Rai+To -RCAT ctim. dt

A: Laplace transform of derivative: If the Laplace transform of function f(t) is F(s), then Laplace…

Q: 12. Find the laplace transfey of pesiodic signal *×せ) 2. 2.

A: To find :              We need to find the Laplace transform of the periodic signal.  When the…

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

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Q: use the Laplace frans forme to solve U - U = 100 u (Xi0) = ut (Xio) =uCoit) %3D %3D limu( X; t ) =0,…

A: The partial differential equation given to us is as follows: utt-uxx=100, x>0, t>0 With the…

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4yHx²j +42?yk. 5: 112. div F= curl F=

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Q: What

A: We use definition of Laplace Transform.

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: The divergence of the vector F = a²yî + æyz} – a*y°k is x2 y? k is -

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Q: Suppose that u = Va2 – y? and v = arcsin() where x-y 0 and- . Which of the following is/are true? A.…

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Q: a/ Q ((Laplace)) 1 A²² [5 (5²+25+5)]

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Q: (a) 3y' In (u) dy

A: We will use the ILATE rule in this example to solve the integral and for solving we use the formula…

Q: 6. If F = Pi + Qj + Rk, prove that div (curl F) = 0

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Q: find laplace of f(x,y,z)=2x3y2z2

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Q: determine laplace of  L{5 - 3t + 4*sin(2t) - 6*exp(4t)}

A: We know for any function f , the Laplace transform f(t) denoted by L { f(t) } is defined by the…

Q: Evaluate Laplace of [9e^-5t + 2e^3t + 6t^3 - 10]

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Q: Find Laplace operator for functier F = 2x' y? zZ %3D

A: The given function is F=2x3y2z2To find its laplace operator

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

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

Q: Find the Laplace of f(t) = (e-3t - e5t )2

A: To Find L(e-3t-e5t)2: Expand (e-3t - e5t )2: (e-3t-e5t)2=e-3t2-2(e-3t·e5t)+e5t2…

Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (1,2) to (3,6).

A: we have to find the work done by the given force

Q: Tet (r, P) be a Laplace space with (a) I s21 = 6 (eia fair Cube) and (6)]2|=7 6 (eig. fair Cube) and…

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Q: Bw (s+a)2+w2

A: Ti find the inverse Laplace transform of the function F(s)=Bw(s+a)2+w2

Q: Find laplace i'nvers 35+3 F(s) =

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Q: biveniJN/AN, Dis the midpoint of JA Prove: AJON E A ADM A.

A: Solved below

Q: Find Laplace treinsform for Y +2 Y + 17 y=0 Y() = 0 Y(0) = 12

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Q: Show that each function satisfies a Laplace equation. ƒ(x, y, z) = x2 + y2 - 2z2

A: Again differentiating with respect to x, we get Now partially differentiating given function with…

Q: Let F = . [[ curlF d5 ,where Use Stokes' Theorem to evaluate S consists of the top and the four…

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Q: re-2t 4t 3.

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Q: Verify . that the. functrun. u= 1+y. t.2? sais fies the thredimensianal.aplace eg. Ux. +Uyy +Uzz=o

A: Given u=1x2+y2+z2

Q: Let T(r,s,t) = (r cos(s) sin(t), r sin(s) sin(t), r cos(t)) Find the Jacobian of T at (3, π/4, π/3)

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Q: Find curl(zi + xj+ yk).

A: Using definition of curl of vector.

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

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Q: Find the dircctional deriu atrue Du f(-3,-1,3) for the function f Cxiy,2) =xy + yz +ZX in the…

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Q: Let F . // curlF d5, where Use Stokes' Theorem to evaluate S consists of the top and the four sides…

A: Given function is F=xyz,xy,x2yz Now calculate the curl F curl…

Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: L{t2e-tsin2t} fonksiyonunun Laplace dönüşümünü bulunuz?

A: We shall first find L [t2 sin(2t)] Consider  L [t2 sin (2t)] = (-1)2 d2ds2 L [sin (2t)]= d2ds2 L…

Q: Solve The Fol/ ewing DiFFerentrul eaquation Using LapLace Trunsform. باتهام مريقه لابا ی 9 - 29 +y…

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Q: by using laplace trans form; s-IVe y+29+5y%3De" Sin(x) y l0) = 0

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Q: If f=x yi- 2xz}+2yz k, find curl F at (1, 1, 1).

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Q: Q2/ Use Laplace properties to find L{S e3u (2sin? u - 1)du } .

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Q: Hiwi fined the curvature for each the Fllbwing vector function Pt) =(44,-t, 2f>

A: Curvature of the 3d-vector

Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

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Q: Fnd the differentnad dy of the functen, sh Cx)

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Q: Find div F and curl F if F(x, y, z) = 8y°z³i – 11x*z°j – 3xy°k.

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Q: Use the laplace trans form to selve y- Hy'+ 4y=1 it Octci and o if +>\, yro)=0, y'lo) = I. (a)…

A: given differential equation is                                                   y''-4y'+4y=1,…

Q: Let xe C and ye show that <xiy= y* AX is que inmer product if A is hermitian positive def iwite

A: Let x∈ℂm and y∈ℂm To prove that x,y=y*Ax is an inner product if A is Hermitian positive definite.…

Q: Without using the shift formula prove that Laplace of f (t) = e**-atcos wt is w**2/((s+a)**2+w**2)

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