\[ y'(x)=x^2 \sqrt {x^2+3 y(x)}+\sqrt {x^2+3 y(x)}+x^3 \sqrt {x^2+3 y(x)}-\frac {2 x}{3} \] ✓ Mathematica : cpu = 0.307955 (sec), leaf count = 65
DSolve[Derivative[1][y][x] == (-2*x)/3 + Sqrt[x^2 + 3*y[x]] + x^2*Sqrt[x^2 + 3*y[x]] + x^3*Sqrt[x^2 + 3*y[x]],y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{192} \left (9 x^8+24 x^7+16 x^6+72 x^5+96 x^4-72 c_1 x^4-96 c_1 x^3+80 x^2-288 c_1 x+144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.294 (sec), leaf count = 30
dsolve(diff(y(x),x) = -2/3*x+(x^2+3*y(x))^(1/2)+x^2*(x^2+3*y(x))^(1/2)+x^3*(x^2+3*y(x))^(1/2),y(x))
\[c_{1}+\frac {3 x^{4}}{8}+\frac {x^{3}}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0\]