2.311   ODE No. 311

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\[ 4 \text {Global$\grave { }$x}^3+9 \text {Global$\grave { }$x}^2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\left (3 \text {Global$\grave { }$x}^3+6 \text {Global$\grave { }$x}^2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-3 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+20 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3\right ) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+6 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2-\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3=0 \] Mathematica : cpu = 0.169236 (sec), leaf count = 2201

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}}{20}+\frac {1}{2} \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}-\frac {1}{2} \sqrt {-\frac {659 \text {Global$\grave { }$x}^3}{500 \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}}-\frac {39 \text {Global$\grave { }$x}^2}{50}-\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}-\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}}{20}+\frac {1}{2} \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}+\frac {1}{2} \sqrt {-\frac {659 \text {Global$\grave { }$x}^3}{500 \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}}-\frac {39 \text {Global$\grave { }$x}^2}{50}-\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}-\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}}{20}-\frac {1}{2} \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}-\frac {1}{2} \sqrt {\frac {659 \text {Global$\grave { }$x}^3}{500 \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}}-\frac {39 \text {Global$\grave { }$x}^2}{50}-\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}-\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}}{20}-\frac {1}{2} \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}+\frac {1}{2} \sqrt {\frac {659 \text {Global$\grave { }$x}^3}{500 \sqrt {-\frac {39 \text {Global$\grave { }$x}^2}{100}+\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}}-\frac {39 \text {Global$\grave { }$x}^2}{50}-\frac {\sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}-\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 \text {Global$\grave { }$x}^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 \text {Global$\grave { }$x}^6+351 e^{c_1} \text {Global$\grave { }$x}^2+\sqrt {3} \sqrt {-67037 \text {Global$\grave { }$x}^{12}+185406 e^{c_1} \text {Global$\grave { }$x}^8-83733 e^{2 c_1} \text {Global$\grave { }$x}^4+32000 e^{3 c_1}}}}}\right \}\right \}\]

Maple : cpu = 0.151 (sec), leaf count = 50

\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( {x}^{4}{{\it \_C1}}^{4}+3\,{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+3\,{{\it \_C1}}^{2}{{\it \_Z}}^{2}{x}^{2}-{\it \_C1}\,{{\it \_Z}}^{3}x+5\,{{\it \_Z}}^{4}-1 \right ) }{{\it \_C1}}} \right \} \]