Q2)A) If U (x,y)%3DXY-sin n is a function and x,y are function of r,9 defined as follow x =r cos 9 y =r sin 9 find Jacobians matrix ?

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

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Q: a) f(z) = 2x + ixy2 b) f(z) = x² +iy2 %3D c) f(z) = e*e¯y

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Q: 6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of…

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Q: Q2. Consider the ODE Using u = y ¹, we get A) u' - xu = sin x B) u + 2xu = - 2 sin x C) u + xu = sin…

A: The given differential equation is       y’ - xy = y2sin x    . . . . . . . . . . . . (1)    Now, we…

Q: Which functions form the basis of solutions for the ODE y – y" – y" +y' (x) = 0? O {1, e ?, e², æe }…

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Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

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Q: əz Use Chain Rule to determine and where

A: We have to use chain rule step by step.

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: y" = 5sin (2z) denkleminin çözümü aşağıdakilerden hangisidir? %3D

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Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

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Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: (L[u],v ) = ( Au, v)) = (Au)"C v = u"A"C v, (u,L*[v]) = (u, A* v) = u"MA* v. (9.5) Comparing these…

A: Given: Lu,v=Au,v=AuTCv=uTATCv u,L*v=u,A*v=uTMA*v   To prove: A*=M-1ATC

Q: mit A === 1 5 3 -1 2 4 Az = y 2 -1 1 und y= -3 3 3

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Q: (b) Determine all functions f=u+ iv that are analytic in the whole plane and has the property that…

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Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: Explain the conditions for the origin a node of the system x' = Ax?

A: The system of the first order differential equations x'=Ax is homogeneous and the matrix A is an n×n…

Q: 5. What are the coordinates of the JNBS if J'(-2, 4), N'(3, 5), B'(2, 3), and S'(0, 2) after R(90".…

A: Given: J'(-2,4) , N'(3,5), B'(2,3) and S'(0,2)

Q: Find the equations of the reflection in the line y=x+1. a) x' = y - 1 , y' = x + 1 b) x' = x - 1 ,…

A: Given: Equations of the reflection in the line : y = x + 1

Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. @ y = (c,+cx)e¯* + cze -2r + e*(c_,cosr + c zsinx)…

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Q: bj f(x,y)= еху cЈ fexiy>= x cosx cобу p² d.j fexiys= (x'y 2) log (x'ty ?).

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Q: - Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in…

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Q: Let X'Y' -system be obtained from XY –system by a rotation through 45°. Describe the equation 2x2 +…

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Q: choose the appropriate answer

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Q: Use implicit differentiation to find dy/dx. 18) y cos = 4x + 4y - y sin A)- cos B) sin 4y 4y2 D)-…

A: 18.we have y cos(1y) =4x+4y⇒dydx(cos(1y) )+ysin(1y)×1y2dydx…

Q: 5) f(x.y)= *+y

A: We are solving the first question and for the next question post the question again andalso mention…

Q: Cosx 0 sinx 1. Solve for x: sinx 0. COSX sinx - cosx 1 sinx+cosX

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Q: Let x' = (1, 1, 3) and y' = (-2, 0, -2). calculate the angle between x and y

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Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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Q: 3) le w= u(x,y)+ iv(xiy) and I=X+ a) for function w show the providing the condition of Vu. Vv =O…

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

Q: Question 2 If z=f(u, v) where u-0.5(x² - y²) and v- xy, show that 8²2 8²z = 2(²-0) 82z əx² +45 2 0…

A: The given function is z=f(u,v) where u=0.5(x2-y2) , v=xy. To Prove:…

Q: for the functions below: a) if y-sinu, u-3x+n find dy/dx at point(0,1) b) Find for the function y =+…

A: we are given: y=sin u and u=3x+π ⇒y=sin (π+3x)=- sin 3x ⇒dydx=-3 cos 3xdydx(0,1)=-3 cos 3(0) =-3…