%3D iv) if zy = (x)-1 then zx + Zy = h.x + y c.-z (x + y) d. z² (x – y)

Q: y = = Vx, 1s xS 8 Intograte ith

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Q: Find d2y/dx2 implicitly in terms of x and y.

A: Implicit differentiation involves the treatment of one of the variables as a function of another and…

Q: Not sure how to find the domain and range.

A: Given function are as below

Q: f(z) = 4z and g(z) = 8z² . e them by comma)

A:

Q: 3x2 +- 8(y + 1) = 0 dy y+1 C 3(: 100 - designed by freepik 24C X=Yi+(x20)

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Q: y = 8e*, on x e [0, 2]

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Q: 4. у" — 2у'+у %3D хе* — е" x’e* Ans. y= c,e* + c2xe* + 6. x²e* 2

A: Solution

Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: XI. 6 F dF where F = (x³ – y, x + e') and C is triangle with vertices (0,0), (3,0), (4,2).

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Q: Find dy for the given values of x and ∆x. ; y = 2x3 + x2 - 4x; x = 2, ∆x = -0.2

A: Find dy for the given values of x and ∆x.

Q: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

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Q: (D^3 - 2D^2 + D) y= xe^x + 1, y(0) = y'(0) = 0, y''(0) = 1. By inspection method.

A: We are given a third order non-homogeneous linear ordinary differential equation as : y''' - 2y'' +…

Q: If xy2 3x2y + C, then what is the value of C at (2,2)?

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Q: 13. f(x, y) = x³ – y³ – 2xy + 6 %3D

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Q: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: findthe solutionof the differenta eqration- dy 2X+y-) X 4X+2Y+5

A:

Q: 5 Given yz - Y1 = m(x2 – x1). Soive for x2- %3D

A: Given y2-y1=m(x2-x1)

Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

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Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: Calculate the LOS of y = -x² + 2x + 4 LOS is x = a is b is ,c is

A: We have to find the line of symmetry and values of a, b, c in the given question.

Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: 3. y = x³ – 3(x² + w²) 4. y = x7 + V7x - 1 TT + 1

A: Differentiation wrt x

Q: A. In each exercise, obtain the family of solution. 2. (x-y)(4x + y) dx + x(5x - y) dy = 0

A: Given differential equation is first order homogeneous differential equation which can be solved by…

Q: 3x e The y, of y"-6y'+9y = x2 by using variation of parameters is: .A Y,(x) =0 .B 3X Y,(x)= -In(x).…

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Q: he equilibrium pul 12) P(x) = -2x + 8, S(x) = 3x + 2 %3D

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Q: Find the domain of y = vx+6. %3D 12. O x 2 6 O x > 6 1/6

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Q: %3D Given: 40 elx [y"-y'] = (x+1)(1-e'2X); determine; А) Ур В) Ус

A: Given 40eixy''-y'=x+11-ei2x

Q: 1. (D 2 + 3D + 2)y = 4t 2 By: (a) reduction of order, and (b) variation of parameters.

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Q: 2 da x² – 8x + 17 Integrate: + C

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Q: (D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e*…

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Q: Q4 If z = x In(xy) a3 z a4z Find and əy²əx əx²əy²

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Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

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Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

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Q: Calculate ∂ω/∂z for ω=e -2xe((z^2)y)

A: While calculating partial derivative ∂ω/∂z, all other variable except z will be considered as…

Q: , Affine, or Nonlinear??? x1 + x2 2x3 + 3x2 Y1 ransformation y2 Y3 x1 + x2 + T+x3

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Q: = (y² – z² +3yz – 2x of the following is/a

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Q: is the minimnurm step of the horno gone ous n What X+ xt 2-X ifferential equatian with its solution…

A: The objective is to find y=x2e-x+x3+x2what is the minimum step of the homogenous differential…

Q: Зх-1 4x+2' , find a) R , and b) R(x+h)-R(x) x+2, 3. Given R(x) = E) %3D

A: Given: R(x)=3x-14x+2

Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: 3x The y, of y''-6y'+9y = by using variation of parameters is: .A Y,(x) = -In(x). e 3x 3x -e |

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Q: A. Using the basic formulas, integrate the following: 1. fx(x² +2)²dx 2. S(2V – 3x)²dx 3. fx³Vxdx 4.…

A: Note: As per our guidelines we are supposed to answer only 3 sub parts under one question. kindly…

Q: Specifically a differential equations problem. Question in pic below.

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Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: Use variation of parameters d²y +pdty+94=Fx) plem) to find a particular solution to y" – 2y - 15y =…

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Q: For what values of m does Y = emx satisfy Y" + Y' - 2Y= 0 ?

A: For what value of m does Y=emx satisfy Y''+Y'-2Y=0

Q: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

Q: Find dy for the given values of x and Δx. y = 6x3 - 7x ; x = -3 and Δx = 0.3 .

A:

Q: Solve for fxx, fxy, fyx and fyy given f(x, y) = 2 ln(x − y).

A: The given function is:fx,y=2 lnx-y.We need find fxx, fxy, fyx and fyy