DSolve[Derivative[1][y][x] == (x*(a^3 + a*b^2*x^4 + b^3*x^6 + 2*a^2*b*x^2*y[x]^2 + 3*a*b^2*x^4*y[x]^2 + a^3*y[x]^4 + 3*a^2*b*x^2*y[x]^4 + a^3*y[x]^6))/(a^(7/2)*y[x]),y[x],x]