DSolve[y[x]*(1 + a^2 - 2*a^2*y[x]^2)*Derivative[1][y][x]^2 + b*Sqrt[(1 - y[x]^2)*(1 - a^2*y[x]^2)]*Derivative[1][y][x]^2 + (-1 + y[x]^2)*(-1 + a^2*y[x]^2)*Derivative[2][y][x] == 0,y[x],x]