1.3E: Direction Fields (Exercises)
- Page ID
- 103466
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In Exercises 1–10 a direction field is drawn for the given equation. Sketch a solution for the IVP.
In Exercises 11 - 20 use the slope field generator to construct a solution curve to the given IVP in the indicated rectangular region.
11. \(y'=y(y-1), \quad y(1)=1; \quad \{-1\le x\le 2,\ -2\le y\le2\}\)
12. \(y'=2-3xy, \quad y(0)=0; \quad \{-2\le x\le 2,\ -2\le y\le2\}\)
13. \(y'=xy(y-1), \quad y(0)=1; \quad \{-2\le x\le2,\ -3\le y\le 4\}\)
14. \(y'=3x+y, \quad y(0)=1; \quad \{-2\le x\le2,\ 0\le y\le 4\}\)
15. \(y'=y-x^3, \quad y(1)=1; \quad \{-2\le x\le2,\ -2\le y\le 2\}\)
16. \(y'=1-x^2-y^2, \quad y(0)=0; \quad \{-2\le x\le2,\ -2\le y\le 2\}\)
17. \(y'=x(y^2-1), \quad y(1)=2; \quad \{-3\le x\le3,\ -3\le y\le 3\}\)
18. \(y'= {xy^2\over y-1}, \quad y(0)=3; \quad \{-1\le x\le1,\ 1\le y\le 4\}\)
19. \(y'=\sin y, \quad y(1)=1; \quad \{-2\le x\le2,\ -2\le y\le 2\}\)
20. \(y'={x^2+y^2\over1+x^2+y^2}, \quad y(1)=0; \quad \{-2\le x\le2,\ -2\le y\le 2\}\)


