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Mathematics LibreTexts

14.23: Section 5.6 Answers

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1. y=12x+c1ex+c2xex;{ex,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+ex)+c1e2x+c2ex;{e2x,ex}

5. y=ex(45x7/2+c1+c2x);{ex,xex}

6. y=ex(2x3/2+x1/2lnx+c1x1/2+c2x1/2);{x1/2ex,x1/2ex}

7. y=ex(xsinx+cosxln|cosx|+c1cosx+c2sinx);{excosx,exsinx}

8. y=ex2(2e2x+c1+c2x);{ex2,xex2}

9. y=2x+1+c1x2+c2x2;{x2,1/x2}

10. y=xe2x9+xex(c1+c2x);{xex,x2ex}

11. y=xex(x3+c1+c2x2);{xex,ex/x}

12. y=(2x1)2ex8+c1ex+c2xex;{ex,xex}

13. y=x4+c1x2+c2x2ln|x|;{x2,x2ln|x|}

14. y=ex(x3/2+c1+c2x1/2);{ex,x1/2ex}

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. {sinx,cosx}

22. {ex,x3ex}

23. {xa,xaln|x|}

24. {xsinx,xcosx}

25. {e2x,x2e2x}

26. {x1/2,x1/2cosx}

27. {x1/2e2x,x1/2e2x}

28. {1/x,e2x}

29. {ex,x2}

30. {e2x,x2e2x}

31. y=x4=6x28x2ln|x|

32. y=2e2xxex

33. y=(x+1)4[ex(32x)+7ex]

34. y=x24+x

35. y=(x+2)26(x2)+2xx24

38.

  1. y=kc1sinkx+kc2coskxc1coskx+c2sinkx
  2. y=c1+2c2exc1+c2ex
  3. y=6c1+c2e7xc1+c2e7x
  4. y=7c1+c2e6xc1+c2e6x
  5. y=(7c1c2)cosx+(c1+7c2)sinxc1cosx+c2sinx
  6. y=2c1+3c2e5x/66(c1+c2e5x/6)
  7. y=c1+c2(x+6)6(c1+c2x)

39.

  1. y=c1+c2ex(1+x)x(c1+c2ex)
  2. y=2c1x+c2(12x2)c1+c2x
  3. y=c1+c2e2x(x+1)c1+c2xe2x
  4. y=2c1+c2e3x(1x)c1+c2xe3x
  5. y=(2c2xc1)cosx(2c1x+c2)sinx2x(c1cosx+c2sinx)
  6. y=c1+7c2x6x(c1+c2x6)

14.23: Section 5.6 Answers is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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