a. Determine the temperature u(x,t) in a rod of length L, given the following conditions: aul au = 0, u(x, 0) = f(x дх x=0 ax x=L

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A: Given data:     The expression for the given electrical potential function is: V(x,y,z)=3x2-2xy+xyz.…

Q: The differ en tial equation yʻz + 2y'e* = 0 is (a) linear (b) separable (c) homogeneous (d) exact

A: The given differential equation is: y4x+2y'ex=0

Q: Consider the given closed rectangular box with dimensions x cm, v cm and z cm. Assume that x is…

A: Consider a rectangular box with dimensions x cm , y cm and z cm .…

Q: 3. y = 1+Vx eğrisi, y = 3 – x doğrusu ve eksenler arasında kalan bölgenin koordinat düzleminin 1.…

A: Given the curve y=1+x, and the line y=3-x. Find the area between the curve, line  and bounded by the…

Q: Uxx + Uyy = 0 |u(0, y) = u(x, b) = 0, u(a, y) = u(x, 0) = 1.

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Q: The bending moment, M, varies with distance, x, from one end of a beam according to: 1 wx2 + C1x +…

A: From the given equation. M=-12wx2+c1x+c2    ....1

Q: Find f(2, 1) and f(2.1, 1.05) and calculate Δz, and use the total differential dz to approximate Δz.…

A: Given

Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z? = 16 and x2 + y2 + z2 = 64 in the first…

A: The region E lies between the spheres: x2+y2+z2=16  and  x2+y2+z2=64  in first octant.

Q: Use LT and one other method to find the PS of (x' = y + z + et {y' = z + x + e* (z' = x + y + et…

A: The given system is                                   x'=y+z+ety'=x+z+etz'=x+y+et…

Q: Given z = 17 In(t) and y = 289 t then fir dy d'y dx?

A: Differentiate given function

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Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: Given that Y(t) = x(a) da, where (X(t)} is a WSS process, prove that 2€ sin’ e w S„(@) S„(@). Hence…

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Q: Evaluate (l. yz dV where E lies above the plane z = 0 and below the plane z = y, and inside the…

A: Given, ∫∫∫EyzdV, Where E lies above the plane z=0 and below the plane z=y and inside the cylinder…

Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

Q: Calculate . (x² + x²)e²as, where S is the cylinder with equation x² + y² = 9 for 0 < z < 10.

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Q: given: W = x² + 2y² + 2² x = cos (st) : y - 2s int 35² √+ chain role, find 3 × 502 8 using dw Ət

A: To solve the following problem

Q: 4.x cot (y), where x = v ln(u) and y = 2uv. dz (a) Compute du dz (b) Compute

A: Given:                 z=x3ex-4x cot(y)wherex=vln(u)y=2uv Let's substitute the values for x and y:…

Q: Solve the following heat equation = ut (x, t) u(0, t) = t, u(1,t) = 0, u(x,0) = x². Uxx (x, t) + x…

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Q: let z be the from a paint minimum distance on the gra ph of y= 5€3x/2) to the Origin which is at (0,…

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Q: Solve the boundary-value problem ди k dx? о 0 dt ди u(0, t) = 0, Əx 3D — h(u(1, t) — и), h > x=1

A: Given: To solve the given boundary- value problem, k∂2u∂x2=∂u∂t,       0&lt;x&lt;1,    t&gt;0

Q: 2)dy - ydx = 0 (x + y cot ) dy

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Q: dw Find where w(x, y, z) = xyz + xy, with x(t) = e", y(t) = e¯24 and z(t) = e-9t dt

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Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

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Q: is given by T(x, y, z) = x +y+ z in degrees centigrade. Find the maximum temperature on this…

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Q: 3- show that the diff. equ. is homogeneous and Salve it (2x+34) dx +(y-x)dy = 0

A: To solve the given differential equation

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z?…

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Q: If w= 2e*_lnx find dw/dt , x=In(t^2 +1), y=tan t, z=e^t

A: If w= 2ex lnx Find dw/dt, x=ln(t2+1) dw / dt = [ ∂w/∂x ]  [ dx/dt] + [ ∂w/∂y ]  [ dy/dt]…

Q: Solve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" - 2y' + 2y = 0,…

A: Given differential equation is a homogeneous equation with constant coefficient. We use auxiliary…

Q: dz Find given: dt z = xe", x = tº, y = 1+ 4t

A: Given,          z=xe3y , x=t6 , y=1+4t

Q: Consider that the heat flow is described by the equation Pu + xe2t ди %3D with BC: du(0.t) Ou(3.1)…

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Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

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Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal…

A: The equation is u t…

Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

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Q: A particle of mass m in a rectangular box with a fixed volume has ground state energy E(x, y) (x >…

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Q: In the given DE, cos x + In y+ 0, integrating M (x, y) with respect to x generates a function g (y).…

A: To solve the following differential equation

Q: 2. Suppose that the edge lengths r, y, and z of a closed rectangular box are changing at the…

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Q: T(z, Y, 2) = 1500e 2y

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Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

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Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: A 3 cm length silver bar with a constant cross section area 1 cm" (density 10 g/cm, thermal…

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Q: If p(x, y) is the density of a wire (mass per unit length), then =1p(x, y)ds т — 1+ cos(t), y =…

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Q: uct Theorem. 10. K y KM=

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.