Exercises Construction of Homogeneous Linear Equations Obtain the differential equations satisfied by the given particular s 1. y = 4e2x + 3e-* 2. y = 7- 2x + etx 1 3. y = e3x – 3x – x2 4. y = e3x - 5ex - 1 5. y = x(1 - e*)

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A: Given:-the region bounded by y=sinx, x=0 and y=1revolving about y=1using washer/disk…

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Q: In each part, evaluate the integral, given that SIx - 61, x 2 0 f(x) : x + 6, x < 0 ' %3D

A: The solution is given in the next steps.

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Q: I. Find əx and and (whenever possible) for the following functions. az ne ду 1) w%3D 5x*у — 11ху3 +…

A: 2). The given function is: w=2ytan2x+y-3xsecx2y3   As we know that; The Power law: ddxxn=nxn-1 The…

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A: Concept: Area in polar coordinates: various regions enclosed by such curves can be calculated using…

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Q: 6. Sketch the vector lield diagrams of the following systems of differential equations in the (r,…

A: (a) vector field

Q: 3s 14 82-4s +8 - 3e cos 2t + 4e2" sin2t 3et cos 2t –4e2" sin2t - Option 1 O Option 2 4e2t cos 2t +…

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A: Explained below

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A: To find out the definite integral.

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A: topic- ellipse

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A: Solved below.

Q: Sunecose - Sune=0

A: The objective of the question is solve the given equation.

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Q: iSy dx dy 3.

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A: The given differential equation is:D2-2D-3y=64xe3xWe will solve this by method of undetermined…

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A: We have to find the value of given trigonometric expression.

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Q: 1-x2 So Si S dz dy dx 0. 0.

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Q: ) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x

A: The given equation is y=c1+c2e2x+c3e-3x. We have to eliminate arbitrary constants c1, c2, c3. Since…

Q: 4e". se"ts dx de Let u* 2e*+2, e*. 2 dy =2e*dk 4 du - edx dx 4 p- du hp: T A 3 4 I du Ju 4 du A9 Let…

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Q: 6s – 4 s2 – 4s + 20

A: 6s-4s2-4s+20=6s-4s2-4s+4+16=6s-12+8s-22+16=6(s-2)+8s-22+16=6·(s-2)s-22+(4)2+8·1s-22+16

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A: We have to find changing the surface area

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Q: oint) Use the graph of f(x) shown below to find the following integrals.

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A: To test for convergence and divergence for the given series.

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A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question. Please…

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Q: 1 3. Let f(r, y, z) = Show that Va? + y? + z²° frz + fyy + fz: = 0.

A: answer is in next step

Q: I just want to confirm if my solution is right. Please check. If not, please correct me.

A: You have done a mistake which I have shown in step 3 of this solution. Kindly go through it.

Q: Volume of Solid Revolution(Circular Disk/ Washer Method) Find the volume of the solid generated by…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

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A: Given query is to find the focus of the parabola.

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Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 1 9n2 + 8 n- 1

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Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: (x, y) = (1, –1) { 1 Show that the function f defined by f(x, y) x2 + y (x, y) # (1, –1) x + y is…

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Q: A) What unique characteristic does the graph of y = e have? B) Why does this characteristic make e a…

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Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

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