11.19: A.2.2- Section 2.2 Answers
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1. y=2±√2(x3+x2+x+c)
2. ln(|siny|)=cosx+c;y≡kπ,k=integer
3. y=cx−cy≡−1
4. (lny)22=−x33+c
5. y3+3siny+ln|y|+ln(1+x2)+tan−1x=c;y≡0
6. y=±(1+(x1+cx)2)1/2;y≡±1
7. y=tan(x33+c)
8. y=c√1+x2
9. y=2−ce(x−1)2/21−ce(x−1)2/2;y≡1
10. y=1+(3x2+9x+c)1/3
11. y=2+√23x3+3x2+4x−113
12. y=e−(x2−4)/22−e−(x2−4)/2
13. y3+2y2+x2+sinx=3
14. (y+1)(y−1)−3(y−2)2=−256(x+1)−6
15. y=−1+3e−x2
16. y=1√2e−2x2−1
17. y≡−1;(−∞,∞)
18. y=4−e−x22−e−x2;(−∞,∞)
19. y=−1+√4x2−152;(√152,∞)
20. y=21+e−2x(−∞,∞)
21. y=−√25−x2;(−5,5)
22. y≡2,(−∞,∞)
23. y=3(x+12x−4)1/3;(−∞,2)
24. y=x+c1−cx
25. y=−xcosc+√1−x2sinc;y≡1;y≡−1
26. y=−x+3π/2
28. P=P0αP0+(1−αP0)e−at;limt→∞P(t)=1/α
29. I=SI0I0+(S−I0)e−rSt
30. If q=rS then I=I01+rI0t and limt→∞I(t)=0. If q≠Rs, then I=αI0I0+(α−I0)e−rαt. If q<rs, then limt→∞I(t)=α=S−qr if q>rS, then limt→∞I(t)=0
34. f=ap,where a=constant
35. y=e−x(−1±√2x2+c)
36. y=x2(−1+√x2+c)
37. y=ex(−1+(3xex+c)1/3)
38. y=e2x(1±√c−x2)
39.