a'+3ab? If 3a’b+b³ 3x°y+y' _ x³+3xy² X_ y Prove that a b

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Q: Howin If Z=RCxy) and u=xayg V=x-y show that 3

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Q: 2.3 Find the general solution of p fanx+q tany =lanz

A: Given:   P tanx+q tan y=tanz→           1   is of the form pP+qQ=z:

Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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Q: 2 1-X ie 2=tny then prove that da

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Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

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Q: Solve for z if cosh z = V3i.

A: Simply put cosh z= 1/2(e^z+e^-z)  Then simplify  then finally got quadratic in e^z  then find the…

Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: 3- Vn n=1

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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Z1 "(cos(0, r2 Z2 02) + isin(0, – 02)](z2 # 0). 85. Let z1 = ri(cos 0, + isin 01) and z2 = r2(cos 0,…

A: Given z1=r1cosθ1+isinθ1 and z2=r2cosθ2+isinθ2.

Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: The standard form of 3dy-xydx = 3y3e4x/3  by Bernoulli's equation is:

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Q: 3 of u(a,9) = Cof"( 4y Cof' (+y then provethat ace +4u + Sin2ce=0

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Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: 2.Prove that I (sinwt) : s2+w?

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Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint chow that f (x) = x cos x has a…

A: Given, Cosx =x

Q: 6xsec 3x 2-If y = (tan3x)" prove that = (tan3x)²"| + 2ln(tan3x) %3D %3! tan3x

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Q: ues of M = 1

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Q: Solve for z if cosh z = v3i.

A: Given cosh z=3ι. Expand cosh z to solve for z.             ez+e-z2=3ι              ez+e-z=23ι…

Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

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

Q: I need help doing number 7

A: We start solving the given equations simultaneously.

Q: :Use inverse matsix (by Gauss Jordan an Elimination) to solve the syálem 2x + By +3 = - 1 %3D 2x…

A: Consider the given equations 2x+3y+z=-13x+3y+z=12x+4y+z=-2 The given equation can be written as AX=B…

Q: Compute Sinh Z c (az - z where C 121-1

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Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

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Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: 16) 1. ZDX 2. -X Show Your Work Valid Invalid

A: We have: Z⊃X~X ∴~Z    This can be written as Z⊃X∧~X⊃~Z  Here, p⊃q means "if p then q" This argument…

Q: az given that yz*+x2z3 = eyz ax

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Q: 2 16n |xV8 - x³ dx: 9/3 3 11) Show that

A: Properties of Beta Function:  β(m, n)=∫01xm-11-xn-1dxβ(m, n)=Γ(m)Γ(n)Γ(m+n) ;       m&gt;0,  n&gt;0…

Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

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Q: 2- (a) Using [X, P] = ih, show that [X, PJ = 2ih& and [&, Þ³1= 2ihP. (b) Show that [, p2 = 2in(in +…

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Q: a3z cos(x – 4y) show that a3z 6. For z = дудхду

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Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

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Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: 4.) Ž(1-sin1)* k=0 codh bs nohsrmotru betroupon or to lla bnit: I- 0pibcipojn BwGr p odmgon: 5.) n=2

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Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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Q: Show a complete soluton 2 3 CO-10y 10sin x

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Q: f5cos(1-5x) dr = O - 5sin (1 – 5x) + C O -sin (1 – 5x)+ C 一 sin (1 5x) + C 5 - O sin (1 – 5x) + C…

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Q: 1) LtZ be a solukion (5) of complese mumber then the sinh Z+ Coah z -e is Z=1?

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Q: Show that lm Casy -1 CoSy-1

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Q: 3: Solve ODE Cist Order a. dY

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