How did Maple arrive at the following, implicit solution,

MSimplicitesolution := (-9*y(x)*(-y(x)*x^2)^(1/3)*6^(2/3)*x^2 + 16*_C1*x^(8/3) - 24*x^2 + 6)/(16*x^(8/3)) = 0, 

to the following 'ode',

ODE:= (2/3)*(int[(y'(x)*(x^2)/((x^2) -1)]) =int(-sqrt [2*y(x)])?

'odeadvisor' suggested y=G(x,y'(x), but I could not see how this could be implimented with this equation.

(Unfortunately, I am unable to download the Maple worksheet onto this sheet at this time.  Any assitance

would be appreciated.                

The goal here is to verify if the solution found by Maple is valid for the submitted ODE or not. Following the usual, 'odetest' and simply plugging the solution provided by Maple into the submitted ODE did not inspire confidence, so I am writing to see where I went wrong. The steps which were followed...

restart;
Equation := 2/(3*int(diff(y(x), x)*x^2/(x^2 - 1), x)^(3/2))
            + int(sqrt(2)*sqrt(y(x)), x) = 0:

ImpliciteSol := simplify(expand(dsolve(Equation)[1]));

     1/16*(-9*y(x)*(-y(x)*x^2)^(1/3)*6^(2/3)*x^2+16*_C1*x^(8/3)-24*x^2+6)/x^(8/3) = 0

yofx := simplify(expand(isolate(ImpliciteSol[1], y(x)))); # does not succeed

    (1/16*(-9*y(x)*(-y(x)*x^2)^(1/3)*6^(2/3)*x^2+16*_C1*x^(8/3)-24*x^2+6)/x^(8/3) = 0)[1] = 0

The goal here is to verify if the solution found by Maple is valid for the submitted ODE or not. Following the usual, 'odetest' and simply plugging the solution provided by Maple into the submitted ODE did not inspire confidence, so I am writing to see where I went wrong.