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Mathematics LibreTexts

14.18: Section 5.1 Answers

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1.

(c) y=2e2x+e5x

(d) y=(5k0k1)e2x3+(k12k0)e5x3

2.

(c) y=e3x(3cosx5sinx)

(d) y=ex(k0cosx+(k1k0)sinx

3.

(c) y=ex(73x)

(d) y=ex(k0+(k1k0)x)

4.

  1. y=c1x1+c2x+1
  2. y=2x13x+1;(1,1)

5.

  1. ex
  2. e2xcosx
  3. x2+2x2
  4. 56x5/6
  5. 1x2
  6. (xln|x|)2
  7. e2x2x

6. 0

7. W(x)=(1x2)1

8. W(x)=1x

10. y2=ex

11. y2=xe3x

12. y2=xeax

13. y2=1x

14. y2=xlnx

15. y2=xalnx

16. y2=x1/2e2x

17. y2=x

18. y2=xsinx

19. y2=x1/2cosx

20. y2=xex

21. y2=1x24

22. y2=e2x

23. y2=x2

35.

  1. y"-2xy'+5y=0
  2. (2x-1)y"-4xy'+4y=0
  3. x^{2}y"-xy'+y=0
  4. x^{2}y"+xy'+y=0
  5. y"-y=0
  6. xy"-y'=0

37. (c) y=k_{0}y_{1}+k_{1}y_{2}

38. y_{1}=1,\: y_{2}=x-x_{0};\quad y=k_{0}+k_{1}(x-x_{0})

39. y_{1}=\cosh (x-x_{0}),\:y_{2}=\sinh (x-x_{0});\: y=k_{0}\cosh (x-x_{0})+k_{1}\sinh (x-x_{0})

40. y_{1}=\cos\omega (x-x_{0}),\: y_{2}=\frac{1}{\omega }\sin\omega (x-x_{0})y=k_{0}\cos\omega (x-x_{0})+\frac{k_{1}}{\omega }\sin\omega (x-x_{0})

41. y_{1}=\frac{1}{1-x^{2}}\: y_{2}=\frac{x}{1-x^{2}}\: y=\frac{k_{0}+k_{1}x}{1-x^{2}}

42.

(c) k_{0}=k_{1}=0;\: y=\left\{\begin{array}{cc}{c_{1}x^{2}+c_{2}x^{3}}&{x\geq 0}\\[4pt]{c_{1}x^{2}+c_{3}x^{3}}&{x<0}\end{array} \right.

(d) (0,\infty ) if x_{0}>0, (−∞, 0) if x_{0} < 0

43. (c) k_{0}=0,\: k_{1} arbitrary y=k_{1}x+c_{2}x^{2}

44.

(c) k_{0}=k_{1}=0;\: y=\left\{\begin{array}{cc}{a_{1}x^{3}+a_{2}x^{4}}&{x\geq 0}\\[4pt]{b_{1}x^{3}+b_{2}x^{4}}&{x<0}\end{array} \right.

(d) (0,\infty ) if x_{0}>0, (−∞, 0) if x_{0} < 0


14.18: Section 5.1 Answers is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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