Question: (a) A direction field for the differential equation y' = x2 - y2 is shown. Sketch the solution of the initial-value problem y' = x2

(a) A direction field for the differential equation y' = x2 - y2 is shown. Sketch the solution of the initial-value problem y' = x2 - y2 y(0) = 1
Use the graph to estimate the value of y(0.3).

(b) Use Euler's method with step size 0.1 to estimate y(0.3), where y(x) is the solution of the initial-value problem in part (a). Compare with your estimate from part (a).
(c) On what lines are the centers of the horizontal line segments of the direction field in part (a) located? What happens when a solution curve crosses these lines?

Step by Step Solution

★★★★★

3.49 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a We estimate that when x 03 y 08 so y03 08 b h 01 x 0 0 y 0 1 and Fx y x 2 y 2 So y n y n 1 01... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

786-C-D-E (700).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Sketch a direction field for the differential equation. Then use it to sketch three solution curves. 10. y' - x - y 9. y' -1 + y

(a) Use a computer algebra system to draw a direction field for the differential equation. Get a printout and use it to sketch some solution curves without solving the differential equation. (b)...

(a) A direction field for the differential equation y = y(y 2) (y 4) is shown. Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y (0) = 0.3 (ii) y (0) = 1 (iii) y (0)...

(a) Sketch the direction field for the differential equation y' = x 2 + y 2 1. (b) Use part (a) to sketch the solution curve that passes through the origin

(a) A direction field for the differential equation y = x2 y2 is shown. Sketch the solution of the initial-value problem y = x2 y2 y (0) = 1 Use your graph to estimate the value of y (0.3). (b) Use...

(a) A direction field for the differential equation y9 x2 2 y2 is shown. Sketch the solution of the initial-value problem y9 x2 2 y2 ys0d 1 Use your graph to estimate the value of ys0.3d. (b) Use...

Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point. 12. y' = xy - x2, (0, 1)24. (:1) Use Euler's method with step size...

Consider the direction field from the differential equation y' = -y (a) Use the direction field above to sketch the graph of the solution with initial condition y(0) = -1 B V A. B. C. D. (b) Are...

Now, try changing the values of x and y from 2 and-3 to other constant values. Describe in your Word document how this changes the phase portrait Next, let's consider the 2x2 system (12) This problem...

Math 1152 Project #4 Solving Initial Value Problems using Power Series and the Laplace Transform Due: Tuesday, April 11 Name(s): - - - - - - - - - - - - - - - - - - - - Description - - - - - - - - -...

Scobie Brass Corp. (SBC) is a wholesaler that sells musical instruments to retailers. On February 1 of the current year, S contracts with Pinder Extravaganza,Inc. (PEI) to sell 1,200 trumpets to P...

Sherm & Co. issued 12,100, $1 par value common shares for $91,000 on June 3, 2018. Required a) Write the journal entry to record the transaction. Date Account Title and Explanation Debit Credit...

The is the value of an asset that in the mind of a particular investor is justified by the facts. market value Drowtivatue intrinsle value tehredvive

Prenatal care Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown on the next page, broken down...

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle...

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. 4 1 + 2x 1 + 1/2 x

Describe how the graph of f varies as c varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points...

Slow Ride Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 $ 29,100 1 11,300 2 14,000 3 15,900 4 13,000 5 9,500 The company uses an interest rate of 8 percent on all of...

43415 is incorrect. 434 is incorrect. Please show correct answer. The following table gives the pattern of investment year rates and portfolio rates over a period of time from 2005 up through 2010....

If the spot rate for Canadian dollars is 1.25 dollars equals 1 US $, and the annual interest rate on fixed rate one-year deposits of Canadian dollars is 2.5% and for US$ is 1.5%, what is the...