I don't understand why y= c3(cosay-cotay) when c4=cotay

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: ) Fin d au se Con el Drder Partial Derivative 3 he gven funrtion. fl2.y): In (x) 2) If fla, y,2,w)…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x3y - 3xyz + 9yz2 %3D…

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Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A: Given differential equation denoting the temperature of the rectangular steel sheet…

Q: A rectangular steel sheet is bounded by the axis x 0,y = 0,x = a and y b. The temperature along the…

A: pleas see the next step for solution

Q: |(a) Suppose a particular investor derives utility function - U(x,y) - from owning x units of stocks…

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Q: b) An undamped oscillation under the influence of external: by UTM UTMUTM U m + kr dt2 where r(t) is…

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Q: 2(a) Given that f(x, y) = 6x²y³ – cosx + 5y – siny + 10x, establish I the fact that, the order in…

A: From the given information.   The given function is as follows.

Q: A flexible string of length t is tightly stretched between x = 0,x = n, on x-axis, its ends being…

A: To solve the problem we use the method of Laplace transformation also Laplace inverse transformation…

Q: find a function z = ƒ(x, y) whose partial derivatives are as given, or explain why this is…

A: From both partial derivatives, we try to get a form for f(x,y). On the sin(xy) part we use by parts…

Q: cos(x + y)dx + (3y ^ 2 + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: We have to solve the initial value problem cos(x+y)dx+(3y2+2y+cos(x+y))dy=0 with the boundary…

Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

A: Solution :-

Q: Answers for 10-12

A: We will solve Q-10

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 8yz2…

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Q: Find the first partial derivative of fx , fy and fz of f ( x , y, z ) = 2xyz +  tan x  +  y sin z…

A: Given problem:- Find the first partial derivative of fx , fy and fz of f ( x , y, z ) = 2xyz + tan x…

Q: A rectangular steel sheet is bounded by the axis -0y-0,x-a and y b. The temperature along the edge…

A: Steady state heat equation.

Q: 1st Case (IBVP Summary) (ut = 1.5Uxx, 0≤x≤ 6ft, t> 0 ux(0,t) = 0, ux(6 ft,t) = 0, t> 0 (u(x,0) =…

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Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: a) A flexible string of length is tightly stretched between x = 0, x = π, on x-axis, its ends being…

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0, x = a and y = b. The temperature…

A: Answer is given below

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A:

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A: Given: x=0,y=0,x=a and y=b. The temperature along the edge  at 100°C and other edges are at 0°C The…

Q: What is the solution of given initial value problem? =y + sin t dt2 da + cost dt - dt2 * (0) = 1, a…

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Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

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Q: 11. Show that the function 2ry when r + y + 0 h(r, y) = 0; when r = y = 0 has partial derivatives…

A: Given: h(x,y) =2xyx2+y2;     when x2+y2≠00 ;      when x=y=0 To show that the partial derivative…

Q: 1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) =…

A: please comment if you need any clarification. I done lots work for you.. please put thumbs up.thank…

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: y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 5xy'. Determine…

A: Given differential equation, 5xdydx=x-y,  x=3,y=6 dydx=x-y5x put, y=vx dydx=v+xdvdx now put values…

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 9xyz + 8yz2 syz?…

A: The objective is to find partial derivatives with respect to x, y and z.

Q: 2. Find the first partial derivatives of (a) f(x,y,2)=x°yz* (c) f(x,y;2)= In[}}+ tan "(0=) (b) f(x,…

A: We need to find first partial derivatives.

Q: If z = 3x°y + 2xy“, where x = sin(5t) and y = 4 cos(2t) , dz a) find dt az (Submit the partial…

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Q: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: 21. xy' = 3y +x* cos x, y(27) = 0 22. y' = 2xy + 3x² exp(x²), y(0) = 5 = 4x* %3D %3D %3D %3D 23. xy'…

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Q: 1. If z = f(x, y) has continuous second-order partial derivatives and x = r cos 0, y = r sin 0,…

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Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: • Find the general and particular solution that satisfy boundary condition Boundary Condition 1. (x+…

A: exact differential equation problem....

Q: The first condition allows computation of the spring constant, k. It follows that the damped…

A: we will first open the complementary solution associated with homogeneous part of the equation then…

Q: Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial…

A: Given:       y=arctan3sinx4+5cosx First derivative:     dydx=ddxarctan3sinx4+5cosx…

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

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Q: A rectangular steel sheet is bounded by the axis x = 0,y = 0,x = a and y = b. The temperature along…

A:

Q: 2. Determine the initial value problem for a damped mass-spring system acted upon by a sinusoidal…

A: We will find out the required solution.

Q: Let u (x, t) be the solution of the initial-boundary value problem Ut 0 0, Uz (0, t) = uz (4, t) =…

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Q: Suppose that z = z (x, y) is a function that admits partial derivatives of the first order which…

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: What is the solution of given initial value problem? y+sin t dt d'y dz +cos t (0) = 1, z'(0)-0,…

A: We will find out the required solution.

Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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Q: The two-dimensional Laplace equation = 0 describes the potentials and steady-state temperature +…

A: given,

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A: rectangular steel sheet is bounded by the axis x = 0, y = 0,x a and y = b. The temperature along the…