A.7.4: Section 7.4 Answers

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

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

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

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

5. \(y = c_{1} \cos (\ln x) + c_{2} \sin (\ln x)\)

6. \(y = x^{2} [c_{1} \cos (3 \ln x) + c_{2} \sin (3 \ln x)]\)

7. \(y=c_{1}x+\frac{c_{2}}{x^{3}}\)

8. \(y = c_{1}x^{2/3} + c_{2}x^{3/4}\)

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

10. \(y = c_{1}x+c_{2}x^{1/3}\)

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

12. \(y =\frac{1}{x} [c_{1} \cos (2 \ln x) + c_{2} \sin (2 \ln x]\)

13. \(y = x^{−1/3} (c_{1} + c_{2} \ln x)\)

14. \(y = x [c_{1} \cos (3 \ln x) + c_{2} \sin (3 \ln x)]\)

15. \(y=c_{1}x^{3}+\frac{x_{2}}{x^{2}}\)

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

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

18. \(y=\frac{1}{x^{2}}\left[c_{1}\cos\left(\frac{1}{\sqrt{2}}\ln x \right)+c_{2}\sin\left(\frac{1}{\sqrt{2}}\ln x \right) \right]\)

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