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) $$y'=csc(x+y)-1$$

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

3) $$ycos(y^2)y'-sin(y^2)=0$$

4) $$y'=yln(y)+y$$

5) $$y'=(x^2+y-1)^2-2x$$

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