The general forms of the Painleve ODEs are given by the following:

Painleve_ode_1 := diff(y(x),x,x) = 6*y(x)^2+x;

Painleve_ode_2 := diff(y(x),x,x) = 2*y(x)^3+x*y(x)+a;

Painleve_ode_3 := diff(y(x),x,x) =
diff(y(x),x)^2/y(x)-diff(y(x),x)/x+(a*y(x)^2+b)/x+g*y(x)^3+d/y(x);

Painleve_ode_4 := diff(y(x),x,x) =
1/2*diff(y(x),x)^2/y(x)+3/2*y(x)^3+4*x*y(x)^2+2*(x^2-a)*y(x)+b/y(x);

Painleve_ode_5 := diff(y(x),x,x) =
(1/2/y(x)+1/(y(x)-1))*diff(y(x),x)^2-diff(y(x),x)/x+(y(x)-1)^2/x^2*(a*
y(x)+b/y(x))+g*y(x)/x+d*y(x)*(y(x)+1)/(y(x)-1);

Painleve_ode_6 :=  diff(y(x),x,x)=1/2*(1/y(x)+1/(y(x)-1)+1/(y(x)-x))*
    diff(y(x),x)^2-(1/x+1/(x-1)+1/(y(x)-x))*diff(y(x),x)+y(x)*(y(x)-1)*
    (y(x)-x)/x^2/(x-1)^2*(a+b*x/y(x)^2+g*(x-1)/(y(x)-1)^2+d*x*(x-1)/(y(x)-x)^2);

These ODEs are irreducible. See E.L. Ince. Ordinary Differential Equations, New York: Dover Publications, 1956, 345.