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Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

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Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: ,2x. General solutton ? %3D

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 3) x 5sin 1, y = 4cos t

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

Q: Solve this egeua tion using differenbicel eque bio us ikx -ik X 4 Cx) s AĈ + 13e

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Q: The convolution of e2t ® sin(3t) S is | e2Usin(3t – 3u)du e2usin(3t – 3u)du Se-2usin(30)du…

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

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Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: ー1 B Cos (2 oin (oen 3 + cas の An

A: Sin(A+B)=sinAcosB+sinBcosA

Q: y If z = show that = 0. x + y?*

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Q: KIN T 2 2 6² 6³ 6² 0 0 ¢sinr do dr de

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Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: 2. If z = x° In 2.xy, find at 1,-

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Q: et u = e Sin P= sin sc Lind su using chain Rule

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Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: i =r+ 1+1 1le n de bifureation? on?

A: This is a problem of Dynatic Model, stability Analysis.

Q: In ab 1+ In² y [tan-1 (In y)]dy

A: Given, I=∫lnab1+ln2y1y[tan-1(lny)]dy Take Constant out, as∫af(y)dy=a∫f(y)dy…

Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

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Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: 1 Suppose y = tan ¹æ. Then x = y tan Otan y Oarctan y

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Q: az Find for z = x'y'eV

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Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: Fird XCK) is X(2) = 2くz-)(マ-3) Ans; SC) ャu(k)+と)uck)

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

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Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: Find the indico 6. 2. 3+ 2 1..2+4+8+ 27 t. 4. 3. 12, (4)"- n= %3D1 2.

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Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

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Q: d 1 - (sec-!r) = dx Prove that xVx - 1

A: Let y=sec-1xsec y =xcos y =1x.....1 Thus sin y=1-cos2y=1-1x2=x2-1x2=x2-1x .......2

Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: In GL(2, Z,,). det

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Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

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

Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: 2 I| ysin(xy)dydx Н.W.

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Q: mith Exe:- Jk +3 - tyk+Z +ZYkxi +36Yx =1+2

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Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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