Revolve about the line x= -1, use disk method. (Bound by y=x4, x=0, and y=16. Mark axis of rotation, draw appropriate differential elements on a graph, and lable all the appropriate dimensions and features.)

Q: Determine the Solutions of ke followsing differential eguation ě (5-x) dx Xy dy %3D

A: A separable differential equation is any equation that can be written in the form. y′=f(x)g(y). The…

Q: Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: O For the differential equation -at y" + 2y'- 3y = 6e Determine the solutioo using Laplace t theorem…

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Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: On the ellipse x2+ 9y2 = 9, find d2y / dx2 using implicit differentiation. Final answer may involve…

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Q: (a) Find the differential equation of the family of spheres of radius r with Centre on the xy-plane…

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Q: PART 1 Obtain the differential equation of the family of plane of curves in Mdx + Ndy = 0 format. 1.…

A: equation of straight line through he fixed point P(h,k) is -  y-k =m(x-h)

Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

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Q: Find the differential equation for the family of parabolas with axis parallel to the x-axis and with…

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Q: Find a curve through the origin in the xy- plane whose length is given by 1/2 L = [; (1+ *)"* dx 4

A: The arc length, L of a curve y=f(x) in the interval a,b is calculated using the formula below.…

Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

Q: What is the equation of the slant asymptote for the slope field created by the differential equation…

A: The objective is to find the equation for slant asymptote for the slope field created by…

Q: Find the differential dy of the given function. sec² x dy Read It Need Help?

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Q: dy 2. sec²y secx dx ;y(0)=0

A: The given differential equation is dysec2y=dxsecx and y(0)=0

Q: Solve the problem by using Laplace Trons form +y= Sin 2€ %3D yo) = 0

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Q: If the hydraulic cylinder AB is extending at a constant rate of 1 ft/s, determine the dumpster's…

A: image is attached

Q: Use computer software to obtain a direction field for the given differential equation. Sketch an…

A: Given:       y dy/dx = -x       y(1) = 1

Q: Find the arc length function for the curve y = 2x3/2 starting at the point (1,2). %3D

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Q: In the presence of a uniform electric field a charge accelerates     indefinitely.     until it…

A: In the presence of a uniform electric field a charge accelerates Under the field perpendicular to…

Q: Use computer software to obtain a direction field for the given differential equation. Sketch an…

A: To plot the direction filed with a curve at a given point of the given differential equation using…

Q: What is the arc length of the curve x = (1/2)y2 - (1/4)ln y from y = 1 to y = e?

A: Here, we have given x is a function of y. So, we will use the following formula for finding the arc…

Q: Compute the differential dz of the function. z = a°!l 9,,11 dz

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Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Given Differential equation : y'=x-xy  ,(1,0) dydx=x(1-y) Now we solve the equation by separation of…

Q: Find the differential dy of the glven function. (Use "dx" for dx.) y = 3Vx + dy = Submit Answer

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Q: dy/dx=(x+siny)/(2y-xcosy) is an exact equation

A: Given that dydx=x+sinyy-xcosy we need to check that it an exact equation

Q: Create a slope field of the differential equation dy cos(t) + cos(y) dt and draw solutions…

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Q: The Soluton Curve for a differential equartion of the form an-y= 3n, passes through dy + passes. the…

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Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: Sketch the direction fields for the differential equation y' = y − x = f (x, y), then sketch the…

A: What is Slope Field: Slope fields, also known as direction fields, are graphical depictions of the…

Q: Given: y = (In x)* , find dy/dx.

A: Given, y=logxx take log both side logy=xloglogx now derivate both side…

Q: Find the differential dy of the given function. y = csc 3x Jax dy Need Help? Read It

A: dy = ? dx

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: Show every detail of your solution. Differential equatioens. siny dx + (x - sin? y)dy3D0

A: The given differential equation is: sin y dx+(x-sin2y)dy=0⇒sin y dx=-(x-sin2y)dy⇒dxdy=-(x-sin2y)sin…

Q: Find the general Solutton of differential CGu aton , 3 t.

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Q: 1. Find the differential equation of the family of hyperbolas having center at C(0, k), whose…

A: It is given that the hyperbola having center at C(0,k) and it's transverse axis is parallel to y…

Q: Find the differential and evaluate for the given a and dæ. 47 y = tan a , a = = dx 4 dy Preview TIP…

A: Please refer the attached image for complete solution.

Q: Create a slope field of the differential equation dy = cos(t) + cos(y) dt and draw solutions…

A: Given: dydt=cos(t)+cos(y) To find: Slope field To sketch: The solutions corresponding to y(0)=0.5,…

Q: Starting from the point (-4, 5, 4) reparametrize the curve r (t) = (-4- 3t)i + (5 – 3t)j + (4 + 2t)k…

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Q: 3. Find the arc length of the curve æ = 5 + y3/2 between y = 0 and y = 2.

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Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

A: Please see the explanation below

Q: (a) Consider the direction field of the differential equation dy/dx = x(y – 8)2 - 4, but do not use…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Starting from the point (-3, –1, 1) reparametrize the curve r (t) = (-3+ 3t) i+(-1+2t)j+ (1+ 3t) k…

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Q: Consider the direction field below for a differential equation. U

A: Given,

Q: Find the differential dy of the function y = 4 sin (2x). Provide your answer below: dy=dx

A: Solution

Q: The order and degree of the differential dy equation + respectively, are O 2, 2 O 1,2 O 4, 2 O 2,1

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.