y = x(arctan x)² arctan (x+ (1+x²)arctan x) А. 1+x2 arctan (2x+ (1–x²)arctan x) В. 1-x2 arctan (2x+ (1+x²)arctan x) C. 1-x2 arctan 2x+ (1ux2)e

Q: (c) | Vtan(x) sec (x)dx 3

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Q: B- Find if y = (x²+1)(x+3)²/2 -, x >1. dx X-1

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Q: y(x²-1)dx + (x³+8y-3x)dy =0  when x=0, y=1

A: Given: 3y2(x2-1)dx+(x3+8y-3x)dy=0initial condition is x=0,y=1

Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: -S² √√x" dx -2- ។ (X) 5 JX dx -2

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Q: 9-x² dydx. 2

A: x = 0 r cos θ = 0 θ = π2 x = 322 r cos θ = 322 r = 322 sec θ   y = x r sin θ = r cos θ θ =…

Q: Solve for separable equation xy +5y + 2x + 10 2xy - 10y -x +5 6. 2x + 3 -dy = 0 y - 6

A: The given differential equation is: xy+5y+2x+102x+3dx+2xy-10y-x+5y-6dy=0 To solve the differential…

Q: 7 I √49-x² 49-x²-z² Ľ -V 49-x² 1 √49−x²−z² (x² + y² + z²)¹/2 dy dz dx =

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Q: d- . -x e-(x² +y²) dy dx -(x²+y²) dy dx

A: We can answer one question as per the honor policy. Please resubmit other question as well to know…

Q: 2-x 4x + 4x - -m(4x* + 4x – 3) + In| (2x 2x- – 3 x +1 x(x + 3)(x + 2)(x – 1) 1 (x + 3)*(x – 1)ª I…

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Q: ) ور شم( موم 2 4-x 2 2 4-x 2 x++y¯+z° e - dz dy dx -2

A: To evaluate the below integral. ∫−22∫04−x2∫04−x2−y2e−x2+y2+z23/2dz dy dx

Q: 5-(1+x')(dy-dx)= 2.xydx;

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Q: 1 [ (2 -y - VE) dy 2 – y – 0. 1 | (2-y (2 – y – V9) dy 0, 2 | (x² – (2 – æ)) dæ - 2 [ (2² – (2 – a))…

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Q: 6. (2z – 1)(y – 1)dr + (x+ 2)(x – 3)dy = 0, y(1) = -1

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Q: 15. /7.- dt 16. x+ 3 dx P + f - 21 2r - &r

A: Solution:Given      ∫dtt3+t2-2tFormula:∫dxx=log x+C

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: (a) (Ex) ((Ax --> Bd) --> Ky) (b) (Ex) ~ (Dx v Cy) (c) -(x) (Dy --> (Hx v ~Ga))

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Q: find dy y = etan-1 √x2+1

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Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

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Q: Evaluate the integrals

A: The given integration is: ∫03∫09-x2∫09-x2 dz dy dx Here first to solve the inside integration with…

Q: -2x y" + (e by = 0 (e-* = z) -

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Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: 7. f(x) = sech"(vi-x) 8. y = sech Inx

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Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

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Q: (1) 1-tank x=sech'x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

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Q: Find dy/dx.  X4y1/3 + e7x - y = (x3 - 11)6

A: X4y1/3 + e7x - y = (x3 - 11)6  dy/dx = ?

Q: 1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25…

A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: f(x, y) 3xy-x² - y²

A: See the details solution in below

Q: √x X² 2x-1 dydx

A: The objective of the question is evaluate the double definite integral.

Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: 2 2. y = - ; th derivative 3x+4 3. y = (x)(2x + 1)³, y" 4. y = 2xvx + 3, dy2 dx2 5. y = v3 - 2ax +…

A: Topic = Derivative

Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: (4) (2xcosy+3x²y)dx+(x³ – x²siny-3)dy=0

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Q: 14-2x 1. ! ] dydx 0 2 2. dxdy 0 y 11-r 3. dycx o 1-x 4. [[ dydx 0 0

A: Answer 1: changing dy dx to dx dy; limits of integration: 0 ≤ x ≤  [2 - (y/2)] 2 ≤ y ≤ 4

Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

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Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: 2. (9y-2 +6y-4-y-5+1) dy 3. √ (12x²-x²+x²) dx

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Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: 1-x²-y² /1-x2-y2 1-х2 (x² + y²)dz dy dx -/1-x2

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Q: /25-x2 V25-x2 -y2 1 dz dy dx -/25–x² -V25-x² -y²

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: Number 29. Find the derivative of the function. I'm confused with the simplification part at the end…

A: Obtain the derivative of the function as follows.

Q: (b) Integrate x-³e-l/a², dx

A: Here we can find the answer as below.

Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

A: