DSolve[Derivative[1][y][x] == (Sqrt[a]*c^2 - 2*Sqrt[a]*b*c*x^2 + b*x^3 + Sqrt[a]*b^2*x^4 + 2*a^(3/2)*c*y[x]^2 - 2*a^(3/2)*b*x^2*y[x]^2 + a^(5/2)*y[x]^4)/(a*x^2*y[x]),y[x],x]