1) y = Arcsin(1 – x²) 2) y = Arctan Vx² + 2x 3) y = Arctan /t²-1 + Arccsc t

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

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Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

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Q: 4. |1- sin2y dy 6. y +2)/y- 1) dy (y + 2)/y

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Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: z = sin(6x) sin(5y) az az dy II

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Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

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Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 5 sin“(3t) dt

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Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: (cos 2y - 3x²d²)dx + (cos 2y − 2x sin 2y − 2x³y) dy = 0

A: The differential equation is given as cos 2y - 3x2y2dx+cos 2y - 2xsin 2y-2x3ydy = 0 Compare it with…

Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

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Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: 1) ſ y³ sin(2y) dy

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining questions…

Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: 4In(Arctan x) = 1-y

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Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

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Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

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

Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: sec Vn du in

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Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

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Q: = Solve: Cony siny dx + dy. cosr sinx

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Q: -Tsin(nx)cosh(3y) dx + 3cos(7x)sinh(3y) dy =0

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Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

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Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1 J sec- ztan - zdz

A: Solve the following

Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: Soru 1. (1+ 25)dx + 20* (1 - )dy = 0 ; -) dy = 0 ; + 2ey) dx y(0) = 1,

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)…

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

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Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

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Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: Calculate •3 2x -dx et – 1 - -3 by Gaussian quadrature with n = 3.

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Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

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Q: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

Q: 5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

A: 5. Given integral, ∫ecosθ-sinθ2sec2θ

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

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Q: far 4 (4f² + 3)² dt cos t dt 1 + sin t sec x tan x dx sec x – 1

A: Given:  4 ∫4t2+32 dt5 ∫cos t1+sin t dt6 ∫sec x tan xsec x-1 dx To Find: To evaluate the each of the…