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# Section 7.4 Answers

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