y 3 A' B' D D' C 4 6 x -2 C' -3 B

Q: 8- (y – y) dy

A:

Q: Find y(4) = d4 y/dx4 if y = -2 sin x

A: Given y=-2sin(x)

Q: 5) (x- 4)² + y² = 9 Center Radius

A:

Q: dy = 3x² – 1 and if y= – 1 when × =1, then Y= dx If

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Q: d^2y/dx^2 for y=2x^3-5/x^2

A:

Q: Evaluate: ³²₁₂[z³(x + y)³] dz dy dx

A: Given, ∫-43∫-12∫01z3x+y3dzdydx

Q: Calculate the derivative.

A:

Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: dy ニ 3 x +y-2

A:

Q: •3 fx(2-x) 10. dy dx 0. r2VIn 3 VIn 3 35. •VIn 3 et dx dy

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

Q: dy :- 15x²y and y = 4 when x = -4 dx

A: To solve the initial value problem  dydx = -15 x2ydyy = -15x2 dx

Q: dy 5.) dx -2x +y = ye +y = ye (ye*) ³ 1 е : ²³-7e²ce Ans: y³ 3X ce ³2

A:

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

A:

Q: y(4) – 4y" = 2t² + sinht -

A:

Q: 9) (3x-29 +2) ex+(39-2*-2) dyzo

A:

Q: I It ex 1-ex dx

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Q: dy 2х + (4х + yу — 6) = y | dx

A:

Q: Find y(4) = d4 y/dx4 if y = 9 cos x.

A: Here given Differentiate the above equation (1) with respect to x

Q: Ex; y* + 8y" + 16у %3D0

A:

Q: @3Dy+12 D3=24

A:

Q: dy Suppose 2e-2* and y(1) = 4. dx What is y(2)?

A: Given,  dydx=2e-2x and y(1)=4

Q: Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

A:

Q: dy -1,-if x²+y?=9 then dx 1- 2- y 3-х-у 4- (x+y)/3 2-

A: The equation is given by x2+y2 = 9                                        .........1 To evaluate:…

Q: dy Differentiate implicitly to find 6 5 3) x y+9x = 6y +4 dy

A: A detailed solution is given below

Q: dy Suppose 9 x²– 2 ( 3 x³-2x+3) and y(1) = 3. dx What is y(2)?

A:

Q: dy 34. = ty² +3t²y with y(-1) = 2 %3D dt

A:

Q: d'y dx +8y = 2x – 5 + 8e **, y(0)=-5, y'(0)=3. y"(0)=-4

A: Given the differential equation            y'''+8y=2x-5+8e-2x with initial conditions y(0)=-5,…

Q: dy/dx if y=3x3/2

A: consider y=3x32differentiate w.r.t.x,ddx(y)=ddx3x32           =3 ddxx32            =3×32x12…

Q: 10 10y-y² IN - 10y-y² ex² + y² dxdy

A:

Q: 4х-6 -dx х2-8х+20

A:

Q: (d) y" + 2y' + y = 8 cosh x.

A:

Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

A:

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

A:

Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

A:

Q: dy If dx and y = 14 when x = 1, find y(2). 3x-2 27

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Q: dy 2 y = x3 – 6x3 бх3 — 5; - | dx5

A:

Q: dy If = 3x2 – 1, and if y= –1 when X=1, then Y= dx

A: We need to integrate the given to solve it

Q: y" +2y' + y = t O y = t-2 O y = 1/2 (t) y = t O y = 2t -1

A: To find the particular solution to the given differential equation first write it into operator…

Q: Differentiate. 3 y=2x® - 8x2 +21x+ 9 dy dx ||

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Q: 16. (2+) y dy

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Q: 2.3 - y 5e2, with y(0) = 0 and y'(0) = 1 %3D

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Q: У (4х + у)dx - 2(х? — у)dy 3 0

A:

Q: -3 ³₁₂₁(4x²y - z³) dz dy dx

A:

Q: y = In(x + 3)4

A: As u mentioned to solve 2nd equation, the solution of the same is attached in next step.

Q: r z+9z-2z2+19z-8 (z²+4)² dx

A: Given: ∫x5+9x3-2x2+19x-8(x2+4)2dx first, we perform a long division for the integrand. then use the…

Q: (62 - y+3) dz+ (3y2-a-2) dy= 0

A:

Q: 3 Evaluate: 2₁ (4x²yz - 2 ) dz dy dx 4

A:

Q: ~tu{S} o 1 In(y) dy de

A: We have to find the double integral

Q: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.