Solve the following differential equations via substitution methods. For some, you will have to come up with your own method.
1) y ′ = c s c ( x + y ) − 1 {\displaystyle y'=csc(x+y)-1}
2) y ′ = c s c ( y x ) + y x {\displaystyle y'=csc({\frac {y}{x}})+{\frac {y}{x}}}
3) y c o s ( y 2 ) y ′ − s i n ( y 2 ) = 0 {\displaystyle ycos(y^{2})y'-sin(y^{2})=0}
4) y ′ = y l n ( y ) + y {\displaystyle y'=yln(y)+y}
5) y ′ = ( x 2 + y − 1 ) 2 − 2 x {\displaystyle y'=(x^{2}+y-1)^{2}-2x}
6) y ′ = x 2 y 2 + y x {\displaystyle y'={\frac {x^{2}}{y^{2}}}+{\frac {y}{x}}}
