a(x.y) Find the Jacobian for the transformations x = 3u cos (6v), y = 3u sin (6v) and x = 3u sin (6v), y = 3u cos (6v). a(u,v)

Q: Find the Jacobian of the transformation. x = 5e-Ar sin(20), y = er cos(20)

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Q: a h is transformed to the diagonal form D=T'AT, where h b The matrix A = cos 0 sin e T = - sin e…

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Q: Consider f(t) = (cos t, sin t, t?) and g(x, y, z) = (x² + y² + z², 3x + 4y – 12z) and h = g(f(t)) =…

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Q: tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'-…

A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

Q: Laplace transform of (e-t sin? t) 1 2 (s + 1)(s² + 2s- 4) (s + 1)(s² + 2s + 5) O Option 1 O Option 2…

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Q: What technique should you use to solve the ODE that arises from the Euler's equation associated with…

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: Find the Laplace transform of the equation: y′′−4y=sin2t when y(0)=0, y′(0)=2 choices: a.)…

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Q: Find the Jacobian of the transformation. x = 5e-2r sin(20), y= e²r cos(20) a(x, y) = alr, e)

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

Q: y'1 =-3y1+y2-12t y'2=-4y1+2y2+12t y1(0)=y2(0)=0 find y1 and y2 by laplace transform

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Q: is transformed to the diagonal form D= 1"'AT, where h b The matrix A= %3D cos 0 sin0 T= -sin 0 cos0…

A: Given matrix is A=ahhb and diagonal matrix is D=T-1AT where T=cosθsinθ-sinθcosθ Now…

Q: Ne the equa tion -aplace transforms

A: Given DE is y"-4y'+3y=6e4x  given conditions are y(0)=2 , y'(0)=6 solve the DE by using Laplace…

Q: xy3dx+(y+1)e-xdy=0

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Q: az az and at as Use the chain rule to find z = tan-(x + y°), x = s In(t), y = tes az as az at

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Q: If y " +3y + 9y = 6e3t, y (0) = 0, y/ (0) = 5 what is %3D %3D the Laplace transform of y? 6. s2+3s+9…

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Q: f(sin 3B)(cos3 B)4dB Apply the transformation method

A: Introduction: Integration is accomplished using the reduction formula. Integration by reduction…

Q: solve for Y(s), the Laplace transform of the solution y(t): y'' +6y'+5y=te^t  where y(0)=2 and…

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Q: (3) Let U(w,t) be the Fourier Transform of u(r,t) acting to the variable r. By Applying the Fourier…

A: 3)option B 4) option A 5)option C

Q: In (a) and (b) below, apply the Laplace transformations to solve the equations. (a) d2x/dt2 - 5…

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Q: By using Implicit Function Theorem, find the points (x, y) where the given transformation can be…

A: First we will find all partial derivatives.

Q: Laplace transform of t cos at s² + a² S (s2 – a?)2 (s² – a²)2 | | O Option 1 O Option 2 s² – a? (s2…

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Q: Using Fourier transform to solve the following IVP U=2 u+te-lxl, -0 0 XX u(x, 0)= f(x) u,(x, 0) =…

A: Given: utt=2uxx+e-x;               -∞<x<∞ and t>0 u(x,0)=f(x) ut(x,0)=g(x) utt=2uxx+e-x;…

Q: Solve the Laplace transform: y” – 6y’ + 15y = 2 sin(3t); y(0) = -1 and y’(0) = 1

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Q: Q1-B) suppose x(t) has Fourier transform X(w) = e-@ find Determine transforms of x(2t) and x(t + 1)

A: Fourier transform using properties.

Q: 7. a State the transformations which map y=sin a onto y= 3sin(x +7). b Sketch y = sin a and y 3…

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Q: 1 G(s) = (s + 10)(s + 1) - Find the Z-transform of the system

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

Q: Solve the De as follows via Laplace transformations: y"- (14/3)y" - (55/3)y' + 14y = 0; y(0) = -1,…

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Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

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Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: If y " +2y + 2y = 3t2, y (0) = 0, y (0) = 2, what is the Laplace transform of y? 2 s2+2s+2 s° (s²…

A: Given:y''+2y'+2y=3 t2, y(0)=0, y'(0)=2

Q: Solve the IVP x”+9x = U(t-2)sin[3(t-2)], x(0)=2, x’(0)=0 using Laplace Transforms. Identify xc , xp…

A: The solution is given as

Q: 6.2 Show that the Lorentz-transformations connecting the S' and S systems may be expressed as = x1…

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Q: 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…

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

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Q: 6.) Find the Jacobian of the transformation = u cos 8 - v sin 6, y = u sin 6 + v cos 6

A: Given Data: x=ucosθ-vsinθ ......1y=usinθ+vcosθ ......2   The partial derivative of equation (1) with…

Q: y" + 2y' + 2y = e-t, y(0+) = 2; y'(0+) = 1.

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Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: The input to a linear system x(1) and the impulse response h(t) of the system are given as : x(t)=…

A: Given that x(t)=exp(-2t), h(t)=exp(-t) and t=>0

Q: 3s+10 W(s) = s(s-8)(s-6)²

A: To solve the following problem

Q: 1Byusing the Jacobian Jeber minant transform dx dy to drdo

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Q: Consider the transformation r = psin o cos 0, y =psin o sin 0, z = p cos o. Near what points (r, y,…

A: Let's check all the options one by one. Option 1 -  x = 2 sin90 cos 0 = 2 y = 2 sin90 sin0 = 0 z = 2…

Q: 7) Using Leibniz notation, apply the chain rule to determine given that: dx 1 Y = из and u = x2 + 2x

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Q: y" – 2/ – 3y = 3 – 4e" y(0+) = 2. 3/ (0+) = 3

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Q: Solve the De as follows via Laplace transformations: y"- (14/3)y"- (55/3)y' + 14y 0; y(0) = -1,…

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Q: Suppose z = x sin y, x =. 3s2 + 2t2, y = 4st. az A. Use the chain rule to find az and as as…

A: Chain rule

Q: %3D (b) Applying the Laplace transformation solve y" – 3y – 2y = te-24, with y(0) = 1, y'(0) = 3.

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Q: Laplace transform solve: y'' + 4y'- 5y = u4(t)       y(0)= 0           y'(0) = 0

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Q: Q1-B) suppose x(t) has Fourier transform X(w) = e-w find Determine transforms of x(2t) and x(t + 1)

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Q: 13. Use the chain rule, in Leibniz notation, to find dx dy at the given value of x. а. у %3D Зи? —…

A: We are solving the first three subparts and for the next subparts post the question againand also…

Q: Find the Jacobian of the transformation. x = 5a sin ß, y² 4α cos β

A: By finding first derivatives and determinant as the formula of jacobian you can solve the given…