#### 2.264   ODE No. 264

$2 x \left (x^3 y(x)+1\right ) y'(x)+y(x) \left (3 x^3 y(x)-1\right )=0$ Mathematica : cpu = 0.376884 (sec), leaf count = 680

$\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 = 0.536 (sec), leaf count = 37

$\left \{ y \left ( x \right ) ={\frac { \left ( {\it RootOf} \left ( {\it \_C1}\,{{\it \_Z}}^{98}-14\,{\it \_C1}\,{{\it \_Z}}^{77}+49\,{\it \_C1}\,{{\it \_Z}}^{56}-9\,{x}^{7} \right ) \right ) ^{21}-7}{3\,{x}^{3}}} \right \}$