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) $y^{\prime }=csc(x+y)-1$

2) $y^{\prime }=csc(\frac{y}{x})+\frac{y}{x}$

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

4) $y^{\prime }=yln(y)+y$

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

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