Advanced Engineering Mathematics, 10th Edition

APPENDIX 2

Answers toOdd-Numbered Problems

Problem Set 1.1, page 8

• 1.
• 3. y = ce^x
• 5. y = 2e^−x(sin x − cos x + c
• 7.
• 9. y = 1.65e^−2x + 0.35
• 11.
• 13. y = 1/(1 + 3e^x)
• 15. y = 0 and y = 1 because y′ = 0 for these y
• 17. exp, t = 10¹¹(1n 2)/1.4 [sec]
• 19. Integrate y″ g twice, y′(t) = gt + v₀, y′(0) = v₀ = 0 (start from rest), then , where y(0) = y₀ = 0

Problem Set 1.2, page 11

• 11. Straight lines parallel to the x-axis
• 13. y = x
• 15. mv′ = mg − bv², v′ = 9.8 − v², v(0) = 10, v′ = 0 gives the limit/9.8 = 3.1 [meter/sec]
• 17. Errors of steps 1, 5, 10: 0.0052, 0.0382, 0.1245, approximately
• 19. x₅ = 0.0286(error 0.0093), x₁₀ = 0.2196(error 0.0189)

Problem Set 1.3, page 18

• 1. If you add a constant later, you may not get a solution. Example: y′ = y, In |y| = x + c, but not e^x + c (with c ≠ 0)
• 3. cos ...