Part 2a) Sketch by hand a slope field for the differential equation y' = x/y. Use it to sketch the four solutions that satisfy the initialconditions y(0) = 1, y(0) = -1, y(2) = 1, and y(-2) = 1.Use a grapher to create a slope field for the particular solutions in part (a) and include a screen capture of the slope field.Verify your solutions in parts (a) and (b) by solving the differential equation explicitly. What type of curve is each solutionb)c)curve?

Answered: a) Sketch by hand a slope field for the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Match the differential equation with its direction field. y' = sin(10x) sin(10y) 20) -0.31 1-0.2 \ +0x1 \ \ 0- - 0.2 / /03 -0.3- 0.2 -0.1 0.1 0.2 -0.3 -2 -1 1 -2 -1 1 0.3- Give reasons for your answer. The slopes at each point are independent of y, so the slopes are the same along each line parallel to the y-axis. Note that for y = 10, y' = 0. o y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 0, and y' > 0 for 0 < x < n/10, 0 < y < n/10. O The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for y = 10, y' = 0. o y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 10. o y' = sin(10x) sin(10y) = 0 on the line y = -x + 1/10, and y' = -1 on the line y = -x. | |||
Find the equation of the curve satisfying the differential equation Example 11 : equation dy (1+x²)+ +2xy=4x² and passing through the origin.
The slope field for the equation y'= -x -y is shown below On a print out of this slope field, sketch the solutions that pass through the points (a) (0, 0); (b) (3, 1); and (c) (1,0). From your sketch, what is the equation of the solution to the differential equation that passes through (1,0)? y =
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The population of fish in a lake grows logistically according to the differential equation where t is in years with no harvesting. If the lake has 550 fish and opens to fishing, determine how many fish can be harvested per year to maintain equilibrium. dy/dt=0.1y(1-y/2500) Differential Equations
Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…

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