11.31: A.4.5- Section 4.5 Answers
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1. y′=2xyx2+3y2
2. y′=−y2(xy−1)
3. y′=−y(x2+y2−2x2ln|xy|)x(x2+y2−2y2ln|xy|)
4. xy′−y=−x1/22
5. y′+2xy=4xex2
6. xy′+y=4x3
7. y′−y=cosx−sinx
8. (1+x2)y′−2xy=(1−x)2ex
10. y′g−yg′=f′g−fg′
11. (x−x0)y′=y−y0
12. y′(y2−x2+1)+2xy=0
13. 2x(y−1)y′−y2+x2+2y=0
14.
15. (e) y=5+3x4,(−3/5,4/5)y=−5−4x3,(4/5,−3/5)
17.
18. y=2x2
19. y=cx√|x2=1|
20. y=y1+c(x−x1)
21. y=−x32−x2
22. y=−xln|x|+cx
23. y=√2x+4
24. y=√x2−3
25. y=kx2
26. (y−x)3(y+x)=k
27. y2=−x+k
28. y2=−12ln(1+2x2)+k
29. y2=−2x−ln(x−1)2+k
30. y=1+√9−x22; those with c>0
33. tan−1yx−12ln(x2+y2)=k
34. 12ln(x2+y2)+(tanα)tan−1yx=k