Graphing First Order Linear D.E.'swork on problem number 2 ( y'=x^2cos(y) )on the picture please! please show all your work and upload picture of all your work!!Include the following: Evaluation of one of the questions above along with a brief explanation of which method you used.Make sure you show all of your work. Initial Post PromptYou will begin by selecting one of the following differential equations to construct a slope field for:1. y'2. y = x² cos(y)Along with your slope field you should identify the following and show you obtained:1. Any equilibrium solutions (if there are no equilibrium solutions, state why not)2. The regions of increasing and decreasing slopes3. Draw two solution curves=4xYYour slope field should be drawn by hand. You do not need to do too many slopes, but your field should demonstrate aclear pattern in the rates of change and make it clear how you came to your solution curves.

Consider the differential equation y′=x2cos⁡y.We need to find the equilibrium points and sketch the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Graphing First Order Linear D.E.'s

work on problem number 2 ( y'=x^2cos(y) )on the picture please! please show all your work and upload picture of all your work!!

Include the following:

Evaluation of one of the questions above along with a brief explanation of which method you used.
Make sure you show all of your work.

Initial Post Prompt
You will begin by selecting one of the following differential equations to construct a slope field for:
1. y'
2. y = x² cos(y)
Along with your slope field you should identify the following and show you obtained:
1. Any equilibrium solutions (if there are no equilibrium solutions, state why not)
2. The regions of increasing and decreasing slopes
3. Draw two solution curves
=
4x
Y
Your slope field should be drawn by hand. You do not need to do too many slopes, but your field should demonstrate a
clear pattern in the rates of change and make it clear how you came to your solution curves.

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Graphing First Order Linear D.E.'s

Please read the instructions on the picture and work on problem number 2!

work on problem number 2 ( y'=x^2cos(y) )on the picture please! please show all your work and upload picture of all your work!!

Include the following:

Evaluation of one of the questions above along with a brief explanation of which method you used.
Make sure you show all of your work.

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Firm's production is represented by z=(10(x^(1/2)))*y^(1/2). z=amount of output. x=amount of labor used. y=amount of capital used. Labor cost= 20 dollars per unit, Capital cost= 80 dollars per unit. Part a) 100 units are currently being made as the output. Labor's cost minimizing quantity=20. Capital's cost minimizing quantity=5. Draw a graph of this with both isocosts and isoquants. Part b) The business wants to make the output increase from 100 units to 140 units. In the short run, capital is fixed. What is the amount of labor needed? Show this in your graph in part a. Calculate the new total cost. Part c) In the graph from part a, draw and label a point that shows capital's and labor's cost minimizing level in the long run if the business wants to make 140 units.
sketch the graph with solution f(x,y)= sqrt(16 - x^2 - 16y^2)
Firm's production is represented by z=10x1/2y1/2. z=amount of output. x=amount of labor used. y=amount of capital used. Labor cost= 20 dollars per unit, Capital cost= 80 dollars per unit. Part a) 100 units are currently being made as the output. Labor's cost minimizing quantity=20. Capital's cost minimizing quantity=5. Draw a graph of this with both isocosts and isoquants. Part b) The business wants to make the output increase from 100 units to 140 units. In the short run, capital is fixed. What is the amount of labor needed? Show this in your graph in part a. Calculate the new total cost. Part c) In the graph from part a, draw and label a point that shows capital's and labor's cost minimizing level in the long run if the business wants to make 140 units.

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