Ordinary Differential Equations/Substitution 3

Solve the following differential equations via substitution methods. For some, you will have to come up with your own method.

1) ${\displaystyle y'=csc(x+y)-1}$

2) ${\displaystyle y'=csc({\frac {y}{x}})+{\frac {y}{x}}}$

3) ${\displaystyle ycos(y^{2})y'-sin(y^{2})=0}$

4) ${\displaystyle y'=yln(y)+y}$

5) ${\displaystyle y'=(x^{2}+y-1)^{2}-2x}$

6) ${\displaystyle y'={\frac {x^{2}}{y^{2}}}+{\frac {y}{x}}}$