$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

3. $$\mu (x)=1/x^{2};\quad y=cx\text{ and }\mu (y)=1/y^{2};\quad x=cy$$

4. $$\mu (x)=x^{-3/2};\quad x^{3/2}y=c$$

5. $$\mu (y)=1/y^{3};\quad y^{3}e^{2x}=c$$

6. $$\mu (x)=e^{5x/2};\quad e^{5x/2}(xy+1)=c$$

7. $$\mu (x)=e^{x};\quad e^{x}(xy+y+x)=c$$

8. $$\mu (x)=x;\quad x^{2}y^{2}(9x+4y)=c$$

9. $$\mu (y)=y^{2};\quad y^{3}(3x^{2}y+2x+1)=c$$

10. $$\mu (y)=ye^{y};\quad e^{y}(xy^{3}+1)=c$$

11. $$\mu (y)=y^{2};\quad y^{3}(3x^{4}+8x^{3}y+y)=c$$

12.$$\mu (x)=xe^{x};\quad x^{2}y(x+1)e^{x}=c$$

13. $$\mu (x)=(x^{3}-1)^{-4/3};\quad xy(x^{3}-1)^{-1/3}=c\text{ and }x ≡ 1$$

14. $$\mu (y) = e^{y};\quad e^{y}(\sin x\cos y+y-1)=c$$

15. $$\mu (y)=e^{-y^{2}};xye^{-y^{2}}(x+y)=c$$

16. $$\frac{xy}{\sin y}=c\text{ and }y=k\pi (k=\text{integer})$$

17. $$\mu (x,y)=x^{4}y^{3};\quad x^{5}y^{4}\ln x=c$$

18. $$\mu (x,y)=1/xy;\quad |x|^{\alpha }|y|^{\beta }e^{\gamma x}e^{\delta y}=c\text{ and }x ≡ 0, y ≡ 0$$

19. $$\mu (x,y)=x^{-2}y^{-3};\quad 3x^{2}y^{2}+y=1+cxy^{2}\text{ and }x ≡ 0, y ≡ 0$$

20. $$\mu (x,y)=x^{-2}y^{-1};\quad -\frac{2}{x}+y^{3}+3\ln |y|=c\text{ and }x ≡ 0, y ≡ 0$$

21. $$\mu (x,y) = e^{ax}e^{by};\quad e^{ac}e^{by}\cos xy=c$$

22. $$\mu (x,y) = x^{-4}y^{-3}\text{ (and others) }xy=c$$

23. $$\mu (x,y) = xe^{y};\quad x^{2}ye^{y}\sin x=c$$

24. $$\mu (x,y) = 1/x^{2};\quad \frac{x^{3}y^{3}}{3}-\frac{y}{x}=c$$

25. $$\mu (x)=x+1;\quad y(x+1)^{2}(x+y)=c$$

26. $$\mu (x,y) = x^{2}y^{2};\quad x^{3}y^{3}(3x+2y^{2})=c$$

27. $$\mu (x,y) = x^{-2}y^{-2};\quad 3x^{2}y=cxy +2\text{ and }x ≡ 0, y ≡ 0$$