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7. xy + y = x², x > 0 8.

7. xy + y = x², x > 0 8.

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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Number 7 3.4 show all work
ph the solution to Example 5 by typing and ent plot (exp (-x^2/2) *int (exp(t^2/2),t=0..x)+exp(-x^2/2),x= This graph appears in Figure 3.8. 1.4E 1.2- 0.8 - 0.6- 0.4 0.2 2 3 Figure 3.8 vative EXERCISES 3.4 dy In Exercises 1–12, determine the integrating factor and solve the differential equation. 1. y + y/x? = 0 11. +e'y = e' dt dr 2. y' = y/x - 2, x > 0 12. =r tan 0 + sin 0,0 < 0 < x/ de 3. y' – 2xy = x 4. y' = 4y +2x In Exercises 13–18, solve the initial v 5. y = 1+ y -, x >0 1+2x 13. y' +4y = 2, y(1) = 2 14. 2xy' + y = 1, y(4) = 0 y 2xy 6. y = x² . 1+x2 15. y + = 2, y(0) = 2 x+1 8. xy+y = x2, x < 0 16. y' + 2xy = 1, y(0) = –1 17. y' = cos 2x – y/x, y(1/2) = 0 7. xy + y = x², x > 0 9. (1+ xy) dx – x² dy = 0, x < 0 10. (1 + xy) dx – x² dy = 0, x > 0 18. x(x +1)y' 2 + y, y(1) = 0
Transcribed Image Text:ph the solution to Example 5 by typing and ent plot (exp (-x^2/2) *int (exp(t^2/2),t=0..x)+exp(-x^2/2),x= This graph appears in Figure 3.8. 1.4E 1.2- 0.8 - 0.6- 0.4 0.2 2 3 Figure 3.8 vative EXERCISES 3.4 dy In Exercises 1–12, determine the integrating factor and solve the differential equation. 1. y + y/x? = 0 11. +e'y = e' dt dr 2. y' = y/x - 2, x > 0 12. =r tan 0 + sin 0,0 < 0 < x/ de 3. y' – 2xy = x 4. y' = 4y +2x In Exercises 13–18, solve the initial v 5. y = 1+ y -, x >0 1+2x 13. y' +4y = 2, y(1) = 2 14. 2xy' + y = 1, y(4) = 0 y 2xy 6. y = x² . 1+x2 15. y + = 2, y(0) = 2 x+1 8. xy+y = x2, x < 0 16. y' + 2xy = 1, y(0) = –1 17. y' = cos 2x – y/x, y(1/2) = 0 7. xy + y = x², x > 0 9. (1+ xy) dx – x² dy = 0, x < 0 10. (1 + xy) dx – x² dy = 0, x > 0 18. x(x +1)y' 2 + y, y(1) = 0
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