2. Eliminate the arbitrary constants: x²y = 1 + Cx 1 Add File 3. Obtain the differential eguation of the famibu of

Q: Let y = 4x². Find the change in y, Ay when æ = 4 and Aæ 0.2 Find the differential dy when a = 4 and…

A: Given: y=4x2 From the given data, x1=4 y1=4(4)2 y1=4(16)y1=64 Also given that ∆x=0.2…

Q: Find the differential dy for the given values of x and Δ x. y = 5x 2 - 2x + 3 ;  x = 2 , Δ x = - 1…

A: Given that: y=5x2-2x+3,  x=2  ,  Δx=-16

Q: Eliminate the arbitrary constants (a, b) in the function to obtain the differentialequation. I e =…

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Q: Let y = = 4a?. Find the change in y, Ay when x = 2 and Ax = 0.2 3.2 Find the differential dy when x…

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

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Q: Find the differential dy of the given function.     y = 3x2/3

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Q: Find the general solutions to the given differential eguations y" – 2y' + y = x² – 1

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Q: Write only the corresponding differential operator of y''+8y'-8y=0

A: The general form of linear ordinary differential equation of order n is yn+a1xyn-1+......+anxy=qx.…

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

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Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Given y=A+ln13x20

Q: Perform the indicated multiplication on the differential operator D. Show your full solution.

A: We have to find out

Q: Obtain the particular solution for the following set of differential equa dy = (4x2 + 7xy +2y²)dx;…

A: Given that: x2dy=(4x2+7xy+2y2)dx        and when x=2, y=0

Q: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.04. y = V3x – 2 A. 0.01…

A: Given that: y=3x-2x=2 to x=2.04

Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

A:

Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

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Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A:

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: Use the differential dy to approximate Ay when x changes from x = -3 tox = -2.99. y = x2 + 1 Enter…

A:

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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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: 2. Test the following differentials for exactness: (a) dF = 2xy² dx + 2yx² dy (b) dF = 8x dx (c) dF…

A: The given data is: a dF=2xy2 dx+2yx2 dy       .......(1) For the differential equation dF=Mdx+Mdy…

Q: - Find a differential operator that annihilates the function f (x) = xe4* – 7x

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

Q: If z = x²y, use differentials to determine dz for the quantity (3.01)2(8.02). 72.662 0.662 0.66…

A: To determine dz. Given that z=x2y for the quantity 3.0128.02. Here x=3, dx=0.01, y=8, and dy=0.02…

Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

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Q: v = ) V In(2x-3y

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

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Q: 15. Use differentials to approximate V26.

A: To approximate263

Q: Find the differentials of each of the following. 1. y= 5x* –3x³ +x – 6 1 2. y= - Vx + 3. y= x²(1–…

A: The objective of the problem is to find the differential of each of the following: Consider the…

Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

A:

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: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: 6. If f( x, y) = V x° + 1 y², estimate the value of f( 2.06 , 4.97 ) using the differentials.

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Q: S(«,9) =7+3y Also, find the total differential of the function.

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Q: Find the degree and state whether each of the following differential enuations is linear, if it is…

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Q: HeWal Compute yG), for the differential eguahion

A: The Laplace transform is a particularly elegant way to solve linear differential equations with…

Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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

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Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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Q: 51. grad f = (2x + 3e")7 +3xe'j

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Q: Sohue the fallowing differential eguatious. d'y odx? "(dx) 2 2. cly

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Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: 5. Find the set of functions which are annihilated by the linear differential op- erator L = D°(D –…

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Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: Z = 1+ In(y² + 1) z = xye*²+y?

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Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

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Q: Let W=x*yz.compute the differential dw.

A: