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1- 2xy 7. y = %3D %3D ds e'-2t co dt 9,

1- 2xy 7. y = %3D %3D ds e'-2t co dt 9,

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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In Exercises 11-14, find the solution of the initial value this the casè, + 2xy + h'(y) = x²+ which implies 1 h' (y) = 구 - xy. But this is impossible since the right-hand side depends o- alone. We will see how to solve an equation such as this in EXERCISES 3.3 In Exercises 1-10, determine if the differential equation is exact. If it is exact, find its solution. 1. (3x2 – 4y²) dx – (8xy – 12y³) dy = 0 2. (3xy +4y2) dx + (5x²y + 2x²) dy = 0 3. (2ry + ye*) dx + (x² + e*) dy = 0 4. (2xe +x²ye*y – 2) dx + x'e* dy = 0 5. (2x cos y – x²) dx +x² sin y dy = 0 6. (y cos x+3e* cos y) dx+(sin x– 3e* sin y) dy = 0 13. 2y sin(ry) dx + (2x sz y(0) = 1 14. [ 1- dy + x² + y², 15. Use Maple (or another age) to graph the solutio 16. Use Maple (or another a age) to graph the solution 17. Show a separable differen 18. Show the converse of TheC integrating with respect to x2 - 2xy + 1 1-2xy 7. y = 8. y' x? - y2 ds 9. dt e' - 0-r cos 0 dr 10. do - 2t cos s 19. Determine conditions on a differential equation ax 1 es - t2 sin s r+ sin 0 Cx + is exact and, for a differentia these conditions, solve the difi problem. 11. 1. 2ry dx + (x² + 3y²) dy = 0, y(1) =1 2xe - 3x?y 12. y = ,y(1) = 0 x3- x2ey M I2
Transcribed Image Text:In Exercises 11-14, find the solution of the initial value this the casè, + 2xy + h'(y) = x²+ which implies 1 h' (y) = 구 - xy. But this is impossible since the right-hand side depends o- alone. We will see how to solve an equation such as this in EXERCISES 3.3 In Exercises 1-10, determine if the differential equation is exact. If it is exact, find its solution. 1. (3x2 – 4y²) dx – (8xy – 12y³) dy = 0 2. (3xy +4y2) dx + (5x²y + 2x²) dy = 0 3. (2ry + ye*) dx + (x² + e*) dy = 0 4. (2xe +x²ye*y – 2) dx + x'e* dy = 0 5. (2x cos y – x²) dx +x² sin y dy = 0 6. (y cos x+3e* cos y) dx+(sin x– 3e* sin y) dy = 0 13. 2y sin(ry) dx + (2x sz y(0) = 1 14. [ 1- dy + x² + y², 15. Use Maple (or another age) to graph the solutio 16. Use Maple (or another a age) to graph the solution 17. Show a separable differen 18. Show the converse of TheC integrating with respect to x2 - 2xy + 1 1-2xy 7. y = 8. y' x? - y2 ds 9. dt e' - 0-r cos 0 dr 10. do - 2t cos s 19. Determine conditions on a differential equation ax 1 es - t2 sin s r+ sin 0 Cx + is exact and, for a differentia these conditions, solve the difi problem. 11. 1. 2ry dx + (x² + 3y²) dy = 0, y(1) =1 2xe - 3x?y 12. y = ,y(1) = 0 x3- x2ey M I2
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