#### 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 = 0.379675 (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 = 0.753 (sec), leaf count = 574

$\left \{ y \left ( x \right ) ={\frac {-40353607\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{91}{\it \_C1}+756315\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{84}{x}^{7}+51883209\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{70}{\it \_C1}-108045\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{63}{x}^{7}-29647548\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{49}{\it \_C1}+9261\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{42}{x}^{7}+5764801\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{28}{\it \_C1}-441\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{21}{x}^{7}-352947\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{7}{\it \_C1}+9\,{x}^{7}}{3\,{x}^{3} \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{7} \left ( 5764801\,{\it \_C1}\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{84}-61740\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{77}{x}^{7}-6588344\,{\it \_C1}\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{63}+6615\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{56}{x}^{7}+3294172\,{\it \_C1}\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{42}-378\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{35}{x}^{7}-605052\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{21}{\it \_C1}+9\, \left ( {\it RootOf} \left ( 9\,{x}^{7}{{\it \_Z}}^{98}-49\,{\it \_C1}\,{{\it \_Z}}^{42}+14\,{\it \_C1}\,{{\it \_Z}}^{21}-{\it \_C1} \right ) \right ) ^{14}{x}^{7}+36015\,{\it \_C1} \right ) }} \right \}$