0If z-x"f), show that xZ+JZy=mZ.

Q: Can you explain the question step by step

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A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

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Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

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A: f(x,y)=xy+2y2

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Q: Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

A: We have to find the definite integral using substitution method In place y^2 =t                2y dy…

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Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: Get z = f(x,y), x = es cos t, y= es sin t 2 + əx. 2 2 Show that it's + at. as

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Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

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Q: bounded by Y=x3, V=1x i rotare about X=1

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Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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Q: Let { sin(r-y) |r|+ |y| 0 (x, y) = (0,0) f(x, y) = Is f continues at the origin? Why?

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Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

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A: In this question, the concept of line integral is applied. Line Integral The function to be…

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Q: If F= 26i- zj+ xk , eviulate F×dr along the carv x=cost , y=Sint ,z=2cost for t=0 to t=1

A: The given problem is to evaluate the given line integral of the vector field over the given curve.…

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

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

Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

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Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

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A: Solve the intial value problem using Laplace transferoms

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A: First find the partial derivative of the given function with  respect to x :

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Q: Suppos analyts s? show work. you

A: Given that f is analytic. And z≤1 And f(0)=0 And f(5)≤5 The formula for derivative is,…

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Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

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Q: 1 V1 – x z 1 – at x = 0 x, 2

A: Since you are asking part (c). We are answering only the (c) part for you.…