Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

Q: Let y = 5a2. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4…

A: ∆y = 5(x + ∆x)^2 - 5x^2= 5(x^2 + 2x∆x + ∆x^2) - 5x^2= 5(2x∆x + ∆x^2)= 10x∆x + 5∆x^2 So when x = 4…

Q: Let y = 5x?. Find the change in y, Ay when x = 2 and Ar 0.4 Find the differential dy when a = 2 and…

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Q: Let y = 5a. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and…

A: According to question given y=5x2x=4 and ∆x=0.4We have to calculate the change in y, ∆y

Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

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Q: Find the integrating factor of the following linear differential equatio rt P. 100 dP dt Select one:…

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Q: Provided the integrating factor (IF) = xy2, find the general soution of the differential equation…

A: Multiply the integrating factor in the differential equation to make it exact.

Q: Which of the following function can be used as an integrating factor for the non-exact differential…

A: he have to find the intregating function

Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: 2x,x X, +X, Find the total differential dy, given

A: Introduction: On an open set S, let z=f(x,y) be continuous. Changes in x and y are represented by dx…

Q: (a) Find the differential dy. y = 1/x+1

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Q: Find the general iné egral of the partial differential equation dz he which contains the circles +y…

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Q: Find the efeneral Solutim Of the differential equatim: (0?-40+3)y=x+ee+x?

A: Answer and explanation is given below...

Q: If df = y(xy + 1)dx - xdy, determine if is a state function of the variables x and y, if not, what…

A: Here we have to check that df is exact or not

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ TACHY 1. (D³ - 5D² + 3D + 9)y = 0 2 (D3 D2 1

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Q: • Determine the value of C for the given first order differential dy y(lny-Inx+1) equation dx when…

A: To find:- particular solution of given differential equation

Q: Find the total differential. w = e3y cos(5x) + z5 ||

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Q: Find the total differential of the function. 5x + у f(x, у, 2) y + 3z df =

A: Total differentiation

Q: 1. Find the total differential dw. 2. w = re2u +e-V

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Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

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Q: If y approximate the differential dy when x changes from 64 to 64.07

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Q: Find The complete Solution of the differential eqution y" +24+4y=cosx Subjected to The condition…

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Q: Let y = 4x“. Find the change in y, Ay when x = 3 and Ax Find the differential dy when x = 3 and dæ =…

A: Given that: y=4x2, x=3 and ∆x=0.4

Q: Let 2x2+ 3x+Y a) Find the differential dy when x = 1 and dx=0.1 %3D b) Find the difiea ial dy when…

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Q: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

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Q: For which value of k is the differential equation (x^k+y^k)dx + (2xy)dy = 0 becomes homogeneous?

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Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

Q: The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is…

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Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

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Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: T. Selue the ff. differential epnotion ) xy (xdy tydy) = ky'dy; when yol; x=2

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: Use separation of variables to find the solution to the differential dy y²(4 + t), if y = 2 when t =…

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Q: 8. If y = xi, then the value of the differential dy as x changes from 16 to is (A) * (B) 5 (c) (D)…

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Q: Compute the differential dz of the function. z = a°!l 9,,11 dz

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Q: Estimate Ay using differentials for the given function and the given values of a and dr 2/3 y =xe-,…

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Q: Find the total differential of  w=x3yz+xy+z+3

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Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: Which of the following function can be used as an integrating factor for the non-exact differential…

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Q: 1. Find the total differential dw. x + y +z 3. w = xyz

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Q: Find a general solution of the following differential equation using Laplace transform. y" +y = cost…

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Q: Given y = 4e* + In x, find the differential dy. %3D

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Q: 16. Use differentials (that is, linear approximation) to approximate: V3.9 – e0.05

A:

Q: Step 3 The total differential dz for the function z = x?y is dz = ydx + dy.

A: We need to find dz.

Q: Let y = 4/T. Find the change in y, Ay when x = 4 and Ax = 0.1 Find the differential dy when x = 4…

A: Given:- f(x) =4√x To find :- Change in y , Δ y when x = 4 and  Δ x=0.1  Differential dy when x= 4,…

Q: Find the total differential df to the function f(x, y) = x²y – xy? when x decreases from -2 to -2.01…

A: We will find out the required value.

Q: Find the general solution of the given higher-order differential equatio y(4) + у" + y" %3D 0 y(x)…

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Q: 3. Evaluate the total differential of the below equation at (x, y) = (16, 24), where dx = 1.5 and dy…

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Q: Consider the differential equation dy y= cos T such that for x = sin a da 2.4 2 Let u be the…

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Q: Find the differential equation of the family of curves y = mx + b where m = b.*

A: We have to solve given problem: