\[ 2 y(x) y''(x)-y'(x)^2-3 y(x)^4=0 \] ✓ Mathematica : cpu = 4.27182 (sec), leaf count = 129
DSolve[-3*y[x]^4 - Derivative[1][y][x]^2 + 2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 \sqrt {\text {$\#$1}} \sqrt {1+\frac {\text {$\#$1}^3}{c_1}} \operatorname {Hypergeometric2F1}\left (\frac {1}{6},\frac {1}{2},\frac {7}{6},-\frac {\text {$\#$1}^3}{c_1}\right )}{\sqrt {\text {$\#$1}^3+c_1}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 \sqrt {\text {$\#$1}} \sqrt {1+\frac {\text {$\#$1}^3}{c_1}} \operatorname {Hypergeometric2F1}\left (\frac {1}{6},\frac {1}{2},\frac {7}{6},-\frac {\text {$\#$1}^3}{c_1}\right )}{\sqrt {\text {$\#$1}^3+c_1}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.1 (sec), leaf count = 49
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2-3*y(x)^4=0,y(x))
\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_a}^{4}+\textit {\_a} c_{1}}}d \textit {\_a} -x -c_{2} = 0\]