Q.6 Solve the Laplace equation U+U = 0 U (0,y)=0,U,(z,y) = 0, U(x,0)=2cos3x+3-2sin²x U(x,1)= cos²x-¹+cos4.x, Hint: U(x, y) = a +by+Σ(A, coshny + B sinh ny) cos nx.

Q: 31²+1 dt = Compute:

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: 2. Find the differential. 1 a) z = b) w=2z°ysinx

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Q: Let w = x°y cos(4z). Find the following. a) (x, Y, z) = Əx b) (x, y, z) = dy c) dz (x, Y, z) · (d) -…

A: Topic = Derivative

Q: Evaluate ((A J A) Į B) Į ((A J A) Į B). O A= B O AvB O AOB O AAB

A: Let us start deriving the result by writing truth table ....we will check with all the given…

Q: The equations re + uz – cos(v) - 2 = 0 and u cos(y) + 10x2v – 10yz2 – 1 = 0 can be solved for (u,v)…

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Q: Find dy/dx in following. )y=x' costx + xsin?x -2

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The equations re + uz – cos(v) – 2 = 0 and u cos(y) + 9x?v – 3yz² – 1= 0 can be solved for (u,v) as…

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Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –…

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Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: (c) Given T" = 6x²y³ – cosx + 5y² – siny + 10x² – e-3x," determine (1) T' = S(T")ax T' = S(T")ay…

A: GivenT"=6x2y2-cos x+5y2-sin y+10x2-e-3xwe know…

Q: S(2) = e- f(2): cos 2ry+ie sin 2ry 2. Find the cauchy-riemann equations of rau du dv dv ləx'əy'əx'…

A: Find partial derivative with respect to x and y.  Comparing real and Imaginary part find u and v.

Q: 5. (ex + Iny +) dx +(÷Inx + siny) dy = 0

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Q: dz Calculate for z = 4x² + 3y², x = sin(t), y = cos(t) dt

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Q: Given z=4x² + y2 -2 and C: x=cos t, y= sin t for [0,2] a) Find z'(t) using chain rule (not…

A: ### Part (a): Finding  z'(t)  using the chain ruleGiven the function  z=4x2+y2−2  and the curve  C…

Q: (c) 2ER. > 0, U₂ +2U₂=2 u(2.0) = cos(902).

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Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: Use approbriate ferm of chain rule to fird %3D

A: Given  z=cos(x)sin(y)x=u−vy=u2+v2

Q: Find the velocity and acceleration of a particle whose position function is <(1)=sin(21)+ cos(t)

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Q: 1. F = cos y i+ xyj + yk, A B C D E F О н A. i+j+(y-siny)k B. i+ (siny - y)k C. j (2y-siny)k D. 3i -…

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Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: 3. Find the position and velocity of the particle if its acceleration is a(t)=-cos(t)i – sin(t)j…

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Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: The equations xe + uz – cos(v) - 2 = 0 and u cos(y) + 5x?v- 7yz2 - 1 solved for (u,v) as functions…

A: Given equations are xey+uz-cos(v)-2=0                  (1) and ucos(y)+5x2v-7yz2-1=0           (2)…

Q: How do I solve the laplace(u(t-2)cos(t-2))

A: The Laplace transform formula for translation on the t-axis is given by ℒ{u(t-a) f(t-a)} = e-asF(s),…

Q: The PDE ugy + sin(y) u, = cos(y) Can be reduced to a first order linear equation as: A) uz + cos(x)…

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Q: 8.2 Making the change of variable z=cos(x) in the equation y" - y' cotx - y sen²x = 0,, the equation…

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Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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Q: a. Find the velocity and speed of the object. b. Find the acceleration of the object. 30. r(t) = (…

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…