15: Section 5.2 Answers

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1. \(y = c_{1}e^{−x} + c_{2}xe^{x}\)

2. \(y=c_{1}x+\frac{c_{2}}{x}\)

3. \(y=c_{1}x+c_{2}x\ln |x|\)

4. \(y =c_{1}e^{2x} + c_{2}e^{x}\)

5. \(y=c_{1}e^x+c_{2}xe^x\)

6. \(y =c_{1}x^{1/2}e^x + c_{2}x^{−1/2}e^x\)

7. \(y =c_{1} e^x \cos x + c_{2} e^x \sin x\)

8. \(y =c_{1}e^{-x^2} + c_{2}xe^{-x^2}\)

9. \(y =c_{1}x^{2} + \frac{c_{2}}{x^{2}}\)

10. \(y=c_{1}xe^{-x}+c_{2}x^2e^{-x}\)

11. \(y=c_{1}xe^{x}+{e^{x}\over x}\)

12. \(y=c_{1}e^{x}+c_{2}xe^{-x}\)

13. \(y=c_{1}x^{2}+c_{2}x^{2}\ln |x|\)

14. \(y =c_{1}e^{−x} + c_{2}x ^{1/2}e^{−x}\)

15. \(y =c_{1}e^{x}+c_{2}x^{2}e^{x}\)

16. \(y=c_{1}x^{1/2}+c_{2}x^{1/2}e^{x}\)

17. \(y =c_{1}x^{2} + c_{2}x^{4}\)

18. \(y=c_1e^x+c_2{e^{x}\over x}\)

19. \(y=c_1x^2+c_2 x^{3}\)

20. \(y=c_1\ln |x|+c_2x\ln |x|\)

21. \(y=c_1\sin\sqrt{x}+c_2\cos\sqrt{x}\)

22. \(y=c_1e^x+c_2x^{3}e^x\)

23. \(y=c_1x^a+c_2x^a\ln |x|\)

24. \(y=c_1x\sin x+c_2x\cos x\)

25. \(y=c_1e^{2x}+c_2x^2e^{2x}\)

26. \(y=c_1x^{1/2}+c_2x^{1/2}\cos x\)

27. \(y=c_1x^{1/2}e^{2x}+c_2x^{1/2}e^{-2x}\)

28. \(y=c_1{1\over x}+c_2e^{2x}\)

29. \(y=c_1e^x+c_2 x^2\)

30. \(y=c_1e^{2x}+c_2x^2e^{2x}\)

31. \(y=7x^{2}-6x^{2}\ln |x|\)

32. \(y={-1\over 2}(x+1)e^x+{3\over 2}(x+1)e^{-x}\)

33. \(y=-x^{-2}+x\)

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