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{\displaystyle y'=csc(x+y)-1}
2) y′=csc(yx)+yx{\displaystyle y'=csc({\frac {y}{x}})+{\frac {y}{x}}}
3) ycos(y2)y′−sin(y2)=0{\displaystyle ycos(y^{2})y'-sin(y^{2})=0}
4) y′=yln(y)+y{\displaystyle y'=yln(y)+y}
5) y′=(x2+y−1)2−2x{\displaystyle y'=(x^{2}+y-1)^{2}-2x}
6) y′=x2y2+yx{\displaystyle y'={\frac {x^{2}}{y^{2}}}+{\frac {y}{x}}}