DSolve[-y[x]^2 + a*(x^2 + y[x]^2)^(3/2) + 2*x*y[x]*Derivative[1][y][x] + (-x^2 + a*(x^2 + y[x]^2)^(3/2))*Derivative[1][y][x]^2 == 0,y[x],x]