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Problem 2: Consider first-order differential equation dy/dx = y – y. 1. Comment true/ false on the statement: 'The above differential equation is an autonomous DE.' (Ans: ) 2. Solve for critical points. (Ans: ) 3. Plot the direction field in the interval -2 < x<2 and -2 sys2. Use 40 points in between the intervals of x and 40 points in between the intervals of y. This plot is called a phase potrait! 4. On the same figure, use ode45 to plot the solution curves that pass through each of the indicated points: (a) y(0) = 0.5 (b) y(0) = –0.5. Each of the solution curves should be plotted in the entire interval –2 sx<2

Problem 2: Consider first-order differential equation dy/dx = y – y. 1. Comment true/ false on the statement: 'The above differential equation is an autonomous DE.' (Ans: ) 2. Solve for critical points. (Ans: ) 3. Plot the direction field in the interval -2 < x<2 and -2 sys2. Use 40 points in between the intervals of x and 40 points in between the intervals of y. This plot is called a phase potrait! 4. On the same figure, use ode45 to plot the solution curves that pass through each of the indicated points: (a) y(0) = 0.5 (b) y(0) = –0.5. Each of the solution curves should be plotted in the entire interval –2 sx<2

Advanced Engineering Mathematics
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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Problem 2: Consider first-order differential equation dy/dx = y – y. 1. Comment true/ false on the statement: 'The above differential equation is an autonomous DE.' (Ans: ) 2. Solve for critical points. (Ans: ) 3. Plot the direction field in the interval -2 <x<2 and -2 < y<2. Use 40 points in between the intervals of x and 40 points in between the intervals of y. This plot is called a phase potrait! 4. On the same figure, use ode45 to plot the solution curves that pass through each of the indicated points: (a) y(0) = 0.5 (b) y(0) = -0.5. Each of the solution curves should be plotted in the entire interval -2 < x<2
Transcribed Image Text:Problem 2: Consider first-order differential equation dy/dx = y – y. 1. Comment true/ false on the statement: 'The above differential equation is an autonomous DE.' (Ans: ) 2. Solve for critical points. (Ans: ) 3. Plot the direction field in the interval -2 <x<2 and -2 < y<2. Use 40 points in between the intervals of x and 40 points in between the intervals of y. This plot is called a phase potrait! 4. On the same figure, use ode45 to plot the solution curves that pass through each of the indicated points: (a) y(0) = 0.5 (b) y(0) = -0.5. Each of the solution curves should be plotted in the entire interval -2 < x<2
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