14.23: Section 5.6 Answers
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1. y=1−2x+c1e−x+c2xex;{e−x,xex}
2. y=43x2+c1x+c2x;{x,1/x}
3. y=x(ln|x|)22+c1x+c2xln|x|;{x,xln|x|}
4. y=(e2x+ex)ln(1+e−x)+c1e2x+c2ex;{e2x,ex}
5. y=ex(45x7/2+c1+c2x);{ex,xex}
6. y=ex(2x3/2+x1/2lnx+c1x1/2+c2x−1/2);{x1/2ex,x−1/2e−x}
7. y=ex(xsinx+cosxln|cosx|+c1cosx+c2sinx);{excosx,exsinx}
8. y=e−x2(2e−2x+c1+c2x);{e−x2,xe−x2}
9. y=2x+1+c1x2+c2x2;{x2,1/x2}
10. y=xe2x9+xe−x(c1+c2x);{xe−x,x2e−x}
11. y=xex(x3+c1+c2x2);{xex,ex/x}
12. y=−(2x−1)2ex8+c1ex+c2xe−x;{ex,xe−x}
13. y=x4+c1x2+c2x2ln|x|;{x2,x2ln|x|}
14. y=e−x(x3/2+c1+c2x1/2);{e−x,x1/2e−x}
15. y=ex(x+c1+c2x2);{ex,x2ex}
16. y=x1/2(e2x2+c1+c2ex);{x1/2,x1/2ex}
17. y=−2x2lnx+c1x2+c2x4;{x2,x4}
18. {ex,ex/x}
19. {x2,x3}
20. {ln|x|,xln|x|}
21. {sin√x,cos√x}
22. {ex,x3ex}
23. {xa,xaln|x|}
24. {xsinx,xcosx}
25. {e2x,x2e2x}
26. {x1/2,x1/2cosx}
27. {x1/2e2x,x1/2e−2x}
28. {1/x,e2x}
29. {ex,x2}
30. {e2x,x2e2x}
31. y=x4=6x2−8x2ln|x|
32. y=2e2x−xe−x
33. y=(x+1)4[−ex(3−2x)+7e−x]
34. y=x24+x
35. y=(x+2)26(x−2)+2xx2−4
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