2.1749   ODE No. 1749

\[ 4 y(x) y''(x)-3 y'(x)^2-12 y(x)^3=0 \] Mathematica : cpu = 0.462985 (sec), leaf count = 153


\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \text {$\#$1} \sqrt {1+\frac {4 \text {$\#$1}^{3/2}}{c_1}} \, _2F_1\left (\frac {1}{6},\frac {1}{2};\frac {7}{6};-\frac {4 \text {$\#$1}^{3/2}}{c_1}\right )}{\sqrt {\text {$\#$1}^{3/2} \left (4 \text {$\#$1}^{3/2}+c_1\right )}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {4 \text {$\#$1} \sqrt {1+\frac {4 \text {$\#$1}^{3/2}}{c_1}} \, _2F_1\left (\frac {1}{6},\frac {1}{2};\frac {7}{6};-\frac {4 \text {$\#$1}^{3/2}}{c_1}\right )}{\sqrt {\text {$\#$1}^{3/2} \left (4 \text {$\#$1}^{3/2}+c_1\right )}}\& \right ][x+c_2]\right \}\right \}\] Maple : cpu = 1.522 (sec), leaf count = 57


\[\int _{}^{y \relax (x )}\frac {1}{\sqrt {c_{1} \textit {\_a}^{\frac {3}{2}}+4 \textit {\_a}^{3}}}d \textit {\_a} -x -c_{2} = 0\]