4. (D2 + 2D + 1Jy = 6

Q: 1. If y = 3x + 2x3 - 3x + 2 find Set A. d'y/dx?

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Q: у" — бу' + 9у %3 t'e", y(0) 3D 2, У (0) 3D 17

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Q: (1) If x=t*2 +1and y= t*3, then the second 3 (4t) Option 1

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Q: 5.Find f, L L*(x² + y² )dydxdz

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Q: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: b) - 2y dy

A: Integrate the following.      ∫y4-2y-4y-2dy

Q: (v) er-y de +e**"dy = o

A: We will solve the differential equation by the method of separation of variables.

Q: 1.y" — у' — 2у 3D 7sinh3t — Зcosh3t ; У (0) 3 2, y'(0) = 4

A: The given differential equation is y''-y'-2y=7sinh3t-3cosh3t; y0=2, y'0=4. Calculate the values ys…

Q: d'y 2y If x + y = xy, show that dx2

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Q: IF Y= 2x² + 5x dy and d = 4, find at when x = 3.

A: See this solution in below

Q: d?y 13 으18 + t6/3- t2 + 246 3 Find if y(t) - dt2 3

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Q: 2.) ² - 1) 1 dy (у? —

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Q: 4) 8r dz dy dr

A: Solve the triple integral

Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: 4.z=(y'-2) 3/4-2y ;z= dz dy

A: The given equation is z=y3-24-2y3 The objective is to find dzdy. The product rule for derivates is…

Q: 12 - y+ ] - dy = |+C

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Q: (4x-3) find dy/dх y = (2х-7)6

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Q: @3Dy+12 D3=24

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Q: 15 ven B = Find the components of -3 relative to B. 2

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Q: z· 3°dz

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Q: y"'-3y"+2y'=t+et

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Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: бу — 7 dy J (2y + 1) (4y² + 1) 11.

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Q: f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

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Q: dy 4. x2 + y? = dr xy (Bernoulli DE) %3D

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 7. y Vzy dz + dy = 0

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Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: d. {(x, y)| y = 3x – 8} {cx, y)ly = } x+3 е. %3D x-5

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Q: b) f(x, y)=-2x². + 8x − 3y² + 24y + 7

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Q: у4у? -16у +19 dy (y-2)°

A: This indefinite integral can be solved by the substitution method.

Q: Find the solution. dy 31 +9y=2ty 5/3 dt

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Q: dædydz (b) (1+x + y+ z)*

A: Kindly go through the explanation

Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: {6} = I ( (b) T = [4,9) %3D (c) T = [-4,9] -

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Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: 29. t²y" - 4ty' +6y=0, t>0; y₁(t) = t²

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Q: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

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Q: Vy² – 25 dy y3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: yz 4. II »z dr dy dz Jo

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Q: d) y" -ry +3y = 0 %3D

A: Using power series method.

Q: />(4y++ +9) * dy 12y2-

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Q: ral of the d D- 1)y is

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Q: If Sc F · dř = [c(2x+ 2y² ) dx + (x²y) dy, what is

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Q: どa (en) (2-x)8 y = X+7 FiNo dy

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Q: dy if y = In dæ 3x + 2 \ 1/4 22. Find x2 – 5

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Q: 5. If x-2ry+ 3y² = 8, then dx %3D 8+ 2y -2x (A) 6y-2x Зу - х (В) y-x (C) 113

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Q: 16 2 2 dz dy da + y? 0.

A: We have to write the given integral into cylindrical coordinates.Let x=r Cosθ       y=r Sinθ…

Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: 18.t2y′′−4ty′+6y=0,t>0;y1(t)=t2

A: