To determine To identify: The differential equation that satisfies the given direction field. Explanation From the given figure shows that the direction field is parallel to t axis at y = 2 and slope of direction field is zero i.e. d y d t = 0 . Again, above the parallel line y = 2 i.e. when y > 2 , the slope become negative. Similarly, for y < 2 , the slope become positive. To calculate the direction field corresponding to part (a) is as follows: y ' = 2 y − 1 Substitute the value of d y d t = 0 in y ' = 2 y − 1 . y ' = 2 y − 1 2 y = 1 y = 1 2 Hence, the above condition does not satisfy the given condition. To calculate the direction field corresponding to part (b) is as follows: y ' = 2 + y Substitute the value of d y d t = 0 in y ' = 2 + y . y ' = 2 + y y = − 2 Hence, the above condition does not satisfy the given condition. To calculate the direction field corresponding to part (c) is as follows: y ' = y − 2 Substitute the value of d y d t = 0 in y ' = y − 2 . y ' = y − 2 y = 2 In part (c), d y d t = y − 2 become 0 on y = 2 . The slope d y d t > 0 for y > 2 and the slope d y d t < 0 for y < 2 . Hence, the above condition does not satisfy the given condition. To calculate the direction field corresponding to part (d) is as follows: y ' = y ( y + 3 ) Substitute the value of d y d t = 0 in y ' = y ( y + 3 ) . y ' = y ( y + 3 ) y = 0 , − 3 Hence, the above condition does not satisfy the given condition. To calculate the direction field corresponding to part (e) is as follows: y ' = y ( y − 3 ) Substitute the value of d y d t = 0 in y ' = y ( y − 3 ) . y ' = y ( y − 3 ) y = 0 , 3 Hence, the above condition does not satisfy the given condition

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Chapter 1.1, Problem 15P

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To identify: The differential equation that satisfies the given direction field.

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Elementary Differential Equations

Ch. 1.1 - In each of Problems 1 through 6, draw a direction...Ch. 1.1 - In each of Problems 1 through 6, draw a direction...Ch. 1.1 - In each of Problems 1 through 6, draw a direction...Ch. 1.1 - In each of Problems 1 through 6, draw a direction...Ch. 1.1 - In each of Problems 1 through 6, draw a direction...Ch. 1.1 - In each of Problems 1 through 6, draw a direction...Ch. 1.1 - In each of Problems 7 through 10, write down a...Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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