\[ 2 x \left (x^3 y(x)+1\right ) y'(x)+y(x) \left (3 x^3 y(x)-1\right )=0 \] ✓ Mathematica : cpu = 0.398825 (sec), leaf count = 680
DSolve[y[x]*(-1 + 3*x^3*y[x]) + 2*x*(1 + x^3*y[x])*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [81 \text {$\#$1}^7 e^{\frac {21 c_1}{2}} x^{12}+756 \text {$\#$1}^6 e^{\frac {21 c_1}{2}} x^9+2646 \text {$\#$1}^5 e^{\frac {21 c_1}{2}} x^6+4116 \text {$\#$1}^4 e^{\frac {21 c_1}{2}} x^3+2401 \text {$\#$1}^3 e^{\frac {21 c_1}{2}}-x^{3/2}\& ,7\right ]\right \}\right \}\] ✓ Maple : cpu = 0.864 (sec), leaf count = 78
dsolve(2*x*(x^3*y(x)+1)*diff(y(x),x)+(3*x^3*y(x)-1)*y(x) = 0,y(x))
\[y \left (x \right ) = \frac {9 \RootOf \left (9 x^{7} \textit {\_Z}^{98}-49 \textit {\_Z}^{42} c_{1}+14 \textit {\_Z}^{21} c_{1}-c_{1}\right )^{77} x^{7}-49 \RootOf \left (9 x^{7} \textit {\_Z}^{98}-49 \textit {\_Z}^{42} c_{1}+14 \textit {\_Z}^{21} c_{1}-c_{1}\right )^{21} c_{1}+7 c_{1}}{3 c_{1} x^{3}}\]