2.1853 ODE No. 1853
\[ 40 y^{(3)}(x)^3+9 y^{(5)}(x) y''(x)^2-45 y^{(4)}(x) y^{(3)}(x) y''(x)=0 \]
✓ Mathematica : cpu = 0.0906809 (sec), leaf count = 43
DSolve[40*Derivative[3][y][x]^3 - 45*Derivative[2][y][x]*Derivative[3][y][x]*Derivative[4][y][x] + 9*Derivative[2][y][x]^2*Derivative[5][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_5 x-\frac {4 \sqrt {x (c_3 x+c_2)+c_1}}{c_2{}^2-4 c_1 c_3}+c_4\right \}\right \}\]
✓ Maple : cpu = 0.83 (sec), leaf count = 110
dsolve(9*diff(diff(y(x),x),x)^2*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-45*diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)+40*diff(diff(diff(y(x),x),x),x)=0,y(x))
\[y \left (x \right ) = \int \int \operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\operatorname {RootOf}\left (-20 \ln \left (\textit {\_f} \right )+\int _{}^{\textit {\_Z}}\textit {\_k} \left ({\mathrm e}^{\operatorname {RootOf}\left (81 \textit {\_k}^{2} {\mathrm e}^{\textit {\_Z}}-40 \,{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-20 \,{\mathrm e}^{\textit {\_Z}} \ln \left (5\right )+20 \,{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+27\right )+162 c_{1} {\mathrm e}^{\textit {\_Z}}-20 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2187 \textit {\_k}^{2}-1080 \ln \left (2\right )-540 \ln \left (5\right )+540 \ln \left ({\mathrm e}^{\textit {\_Z}}+27\right )+4374 c_{1} -540 \textit {\_Z} -540\right )}+27\right )d \textit {\_k} +20 c_{2} \right )}d \textit {\_f} \right )+x +c_{3} \right )d x d x +c_{4} x +c_{5}\]