11.58: A.9.2- Section 9.2 Answers
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1. y=ex(c1+c2x+c3x2)
2. y=c1ex+c2e−x+c3cos3x+c4sin3x
3. y=c1ex+c2cos4x+c3sin4x
4. y=c1ex+c2e−x+c3e−3x/2
5. y=c1e−x+e−2x(c1cosx+c2sinx)
6. y=c1ex+ex/2(c2+c3x)
7. y=e−x/3(c1+c2x+c3x2)
8. y=c1+c2x+c3cosx+c4sinx
9. y=c1e2x+c2e−2x+c3cos2x+c4sin2x
10. y=(c1+c2x)cos√6x+(c3+c4x)sin√6x
11. y=e3x/2(c1+c2x)+e−3x/2(c3+c4x)
12. y=c1e−x/2+c2e−x/3+c3cosx+c4sinx
13. y=c1ex+c2e−2x+c3e−x/2+c4e−3x/2
14. y=ex(c1+c2x+c3cosx+c4sinx)
15. y=cos2x−2sin2x+e2x
16. y=2ex+3e−x−5e−3x
17. y=2ex+3xex−4e−x
18. y=2e−xcosx−3e−xsinx+4e2x
19. y=95e−5x/3+ex(1+2x)
20. y=e2x(1−3x+2x2)
21. y=e3x(2−x)+4e−x/2
22. y=ex/2(1−2x)+3e−x/2
23. y=18(5e2x+e−2x+10cos2x+4sin2x)
24. y=−4ex+e2x−e4x+2e−x
25. y=2ex−e−x
26. y=e2x+e−2x+e−x(3cosx+sinx)
27. y=2e−x/2+cos2x−sin2x
28.
29. {e−3xcos2x,e−3xsin2x,e2x,xe2x,1,x,x2}
30. {ex,xex,ex/2,xex/2,x2ex/2,cosx,sinx}
31. {cos3x,xcos3x,x2cos3x,sin3x,xsin3x,x2sin3x,1,x}
32. {e2x,xe2x,x2e2x,e−x,xe−x,1}
33. {cosx,sinx,cos3x,xcos3x,sin3x,xsin3x,e2x}
34. {e2x,xe2x,e−2x,xe−2x,cos2x,xcos2x,sin2x,xsin2x}
35. {e−x/2cos2x,xe−x/2cos2x,x2e−x/2cos2x,e−x/2sin2x,xe−x/2sin2x,x2e−x/2sin2x}
36. {1,x,x2,e2x,xe2x,cos2x,xcos2x,sin2x,xsin2x}
37. {cos(x/2),xcos(x/2),sin(x/2),xsin(x/2),cos2x/3xcos(2x/3),x2cos(2x/3),sin(2x/3),xsin(2x/3),x2sin(2x/3)}
38. {e−x,e3x,excos2x,exsin2x}
39. b. e(a1+a2+…+an)x∏1≤i<j≤n(aj−ai)
43.
45. y=c1xr1+c2xr2+c3xr3(r1,r2,r3 distinct);y=c1xr1+(c2+c3lnx)xr2(r1,r2 distinct);y=[c1+c2lnx+c3(lnx)2]xr1;y=c1xr1+xλ[c2cos(ωlnx)+c3sin(ωlnx)]