d 5. Prove (arccot(x)) dx -1 Be sure to provide a written justification for your work. 1+ x?

Q: 2. Solve the following DE: a. (2x + 2y + 1)dx+ (x+ y– 8) dy=0

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Q: 4x Compute (2x + 4yz) dz dæ dy 1

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Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

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Q: Ɔ) = 1, the solu %D dy + 4 + 4 dx

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Q: In Q5:A/ Find 2xe* cos (e**) dx

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Q: 1. So letet Jo 1+ e* t -dx

A: The given integral,        ∫01ex1+exdx

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Q: In x2/25+ x² dx , we let x= 5sine. T True F False

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Q: Solve the following equation and show that it is exact 3x (xy +2)dx + (x^3 - 2y)dy = 0

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Q: 2. Evaluate (x2 – 1)e" dx T/2 3. Evaluate cos (0) d0. Write your ans"

A: Consider the integral- I=∫01(x2-1)exdx =∫01x2exdx-∫01exdxLet I=I1-I2—(1)Where ,I1=∫01x2exdx and…

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Q: (x² + 6y²)dx – 4xydy = 0,x = 1, y = 1 -

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Q: Solve the following using the method of solving other substitution methods dy 2. dx sin(x – y)

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Q: 1. Find d it dX =x' + Sin xy

A: Note: As per our guideline we are supposed to answer only one question. Since you have asked…

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Q: Evaluate the followings: (1) S" e-2x x² dx (2) S cos® 0 de

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Q: 21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

A: Divergent

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A:

Q: s+3 is equal to s2 – 6s + 45 | A e3tcos6t В e3t (cos6t + sin6t) © e-3t(cos6t + sin6t) D e3t(cosh6t +…

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Q: Solve the following D.E.s d'y dy 4 + 12 у %3D бх — 2 е* (1) - dx2 dx

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Q: dy 4a +9 10. dx

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Q: 33.) Show all steps to evaluate by hand: 4-х2 Vx2 + y2 dy dx

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Q: fsinx cos/x Зл А 256 3 (В 512 (C) None Зл (D) 512 3 E) 256 -dx is equal to

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Q: Solve the following D-E 1) y' +y = sinx dy 2) x - 2y = x°cos4x dx dy 3) x = y + x³ + 3x² – 2x dx

A: **As per bartleby guidelines we are allowed to answer only 1 question or 3 sub parts at a time.…

Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

A: Solution :

Q: 1.) Evaluate In 2 e*2arctan e* dx (1 + e2×) sec(2arctan e*) A.)

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A: Solve for derivative

Q: 4 dy 5. х dx + бу %3D 3хуз 3xy

A:

Q: 3. Show that the equation (x²y)dx + () dy = 0 is exact and then solve it.

A:

Q: Q6A)If y = sin-¹ prove Zyy + 2 = 0

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Q: Solve the following. Additionally, comment on the behavior of the solu- tion(s) as t → o. (a) 3 2 4…

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Q: 3. Which of the following gives if y=sin" (2x)? dx 2 (A) V1-4x 1 (B) V1- 4x 2 (C) V1-4x 1 (D) V1-4x…

A: To find the dy/dx

Q: 2. Evaluate each. (a) sin(y²) dy dr cln(2) -In(5) e2z+y dy dx (b)

A: We use change in order of part a

Q: хуз dx + e** ,3 dy = 0.

A:

Q: Given that ƒ(1) = 5, ƒ′(1) = 4, g(1)= 2, and g′(1) = 3, find

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Q: II. Solve the following first order DE. (x² + y²)dx + xy dy = 0 4.

A: Explanation of the solution is given below...

Q: gèstion 8 If we have to check the DE (5-8y+4xy)dx = (x+2)'dy for Exact then M, !! -8 2(x+2) -8 +4x…

A: We have to solve given problem:

Q: (a) By using the substitution, u = 1+ x*, or otherwise, find x3 dx 1+ x*

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Q: 1. Determine the following: 2 x7 + (2x (2x + 3)a| dx С. 5x3 d. S[sin(3x) – 7e-2*]dx

A: By using integration property, we calculate the following Integral.

Q: Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?

A: Consider the integral  ∫e2xe2x+3ex+2dx

Q: dy Find dæ |(7,9)=(-1,-1) if e sin (x? – xy) = y² – 1.

A: Given,          xsinx2-xy=y2-1

Q: 3. following Solve the dy

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Q: Solve the following using the method of solving Bernoulli Equations. dy 1. dx +? = x²y?

A: Given:         dydx+yx=x2y2 This is of the form dydx+P(x)y=Q(x)yn…