\[ 40 y^{(3)}(x)^3+9 y^{(5)}(x) y''(x)^2-45 y^{(4)}(x) y^{(3)}(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.123873 (sec), leaf count = 43
\[\left \{\left \{y(x)\to c_5 x-\frac {4 \sqrt {x (c_3 x+c_2)+c_1}}{c_2{}^2-4 c_1 c_3}+c_4\right \}\right \}\] ✓ Maple : cpu = 0.921 (sec), leaf count = 110
\[y \relax (x ) = \int \int \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\RootOf \left (-20 \ln \left (\textit {\_f} \right )+\int _{}^{\textit {\_Z}}\textit {\_k} \left ({\mathrm e}^{\RootOf \left (81 \textit {\_k}^{2} {\mathrm e}^{\textit {\_Z}}+20 \,{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+27\right )-40 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (2)-20 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (5)+162 c_{1} {\mathrm e}^{\textit {\_Z}}-20 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2187 \textit {\_k}^{2}+540 \ln \left ({\mathrm e}^{\textit {\_Z}}+27\right )-1080 \ln \relax (2)-540 \ln \relax (5)+4374 c_{1}-540 \textit {\_Z} -540\right )}+27\right )d \textit {\_k} +20 c_{2}\right )}d \textit {\_f} \right )+x +c_{3}\right )d x d x +x c_{4}+c_{5}\]