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9. (x²y + xy-y) + (x²y - 2x²) dy = 0 dx

9. (x²y + xy-y) + (x²y - 2x²) dy = 0 dx

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
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Chapter Review Problems Miscellaneous Problems. One of the difficulties in solving first- order differential equations is that there are several methods of solution, each of which can be used on a certain type of equation. It may take some time to become proficient in matching solution methods with equations. The first 24 of the following problems are presented to give you some practice in identifying the method or methods applicable to a given equation. The remaining problems involve certain types of equations that can be solved by specialized methods. In each of Problems 1 through 24, solve the given differential equation. If an initial condition is given, also find the solution that satisfies it. x³ - 2y 1. 2. 3. 4. 5. ala a aa dy dx 7. X X 1 + cos x 2- sin y 2x + y dy dx 3+3y²-x dy dx dy dx dy dx dy 6. x- dx dy dx = dy dx = = = 3-6x + y - 2xy 2xy + y² +1 x² + 2xy + xy = 1- y, BRASO sin x y(0) = 0 + 2y = y(1) = 0 y(2) = 1 X 2xy +1 8. x² + 2y 9. (x²y + xy - y) + (x²y - 2x²) dy dx =0 10. (x² + y) + (x+e³) 11. (x+y)+(x + 2y) 12. (et + 1). 13. 14. 15. 16. al ala ala 18. dy dx 21. dx dy - e²x + 3y = dy 22. dx dy dx 17. y' = ex+y 19. t ale ale pale alš dy dx + 2y = e-x²-2x, y(0) = 3 = dy dx e-x cos y - e²y cos x -e-* sin y + 2e²y sin x + dy dt dy dx dy dy = 0 dx = y - ye* 20. xy' = y + xey/x dx dy dx 3x² - 2y - y³ 2x + 3xy² = 0, y(2) = 3 2y² + 6xy - 4 3x² + 4xy+3y² + (t+1) y = e²t x+y X x²y + y² x - y = 0 Hint: Let u = x². dy (3y² + 2xy) - (2xy + x²) x dx y(1) = 2 23. 24. xy + y - y²e²x = 0,
Transcribed Image Text:Chapter Review Problems Miscellaneous Problems. One of the difficulties in solving first- order differential equations is that there are several methods of solution, each of which can be used on a certain type of equation. It may take some time to become proficient in matching solution methods with equations. The first 24 of the following problems are presented to give you some practice in identifying the method or methods applicable to a given equation. The remaining problems involve certain types of equations that can be solved by specialized methods. In each of Problems 1 through 24, solve the given differential equation. If an initial condition is given, also find the solution that satisfies it. x³ - 2y 1. 2. 3. 4. 5. ala a aa dy dx 7. X X 1 + cos x 2- sin y 2x + y dy dx 3+3y²-x dy dx dy dx dy dx dy 6. x- dx dy dx = dy dx = = = 3-6x + y - 2xy 2xy + y² +1 x² + 2xy + xy = 1- y, BRASO sin x y(0) = 0 + 2y = y(1) = 0 y(2) = 1 X 2xy +1 8. x² + 2y 9. (x²y + xy - y) + (x²y - 2x²) dy dx =0 10. (x² + y) + (x+e³) 11. (x+y)+(x + 2y) 12. (et + 1). 13. 14. 15. 16. al ala ala 18. dy dx 21. dx dy - e²x + 3y = dy 22. dx dy dx 17. y' = ex+y 19. t ale ale pale alš dy dx + 2y = e-x²-2x, y(0) = 3 = dy dx e-x cos y - e²y cos x -e-* sin y + 2e²y sin x + dy dt dy dx dy dy = 0 dx = y - ye* 20. xy' = y + xey/x dx dy dx 3x² - 2y - y³ 2x + 3xy² = 0, y(2) = 3 2y² + 6xy - 4 3x² + 4xy+3y² + (t+1) y = e²t x+y X x²y + y² x - y = 0 Hint: Let u = x². dy (3y² + 2xy) - (2xy + x²) x dx y(1) = 2 23. 24. xy + y - y²e²x = 0,
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