Internal problem ID [7440]
Book: Second order enumerated odes
Section: section 1
Problem number: 51.
ODE order: 2.
ODE degree: 3.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 124
dsolve(y(x)*diff(y(x),x$2)^3+y(x)^3*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = c_{1} y \left (x \right ) = {\mathrm e}^{\int \operatorname {RootOf}\left (x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_f}^{2}-\left (-\textit {\_f} \right )^{\frac {1}{3}}}d \textit {\_f} +c_{1} \right )d x +c_{2}} y \left (x \right ) = {\mathrm e}^{\int \operatorname {RootOf}\left (x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{i \sqrt {3}\, \left (-\textit {\_f} \right )^{\frac {1}{3}}+2 \textit {\_f}^{2}+\left (-\textit {\_f} \right )^{\frac {1}{3}}}d \textit {\_f} \right )+c_{1} \right )d x +c_{2}} y \left (x \right ) = {\mathrm e}^{\int \operatorname {RootOf}\left (x -2 \left (\int _{}^{\textit {\_Z}}\frac {1}{i \sqrt {3}\, \left (-\textit {\_f} \right )^{\frac {1}{3}}-2 \textit {\_f}^{2}-\left (-\textit {\_f} \right )^{\frac {1}{3}}}d \textit {\_f} \right )+c_{1} \right )d x +c_{2}} \end{align*}
✓ Solution by Mathematica
Time used: 3.023 (sec). Leaf size: 800
DSolve[y[x]*y''[x]^3+y[x]^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (-\text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1+\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},-\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (\sqrt [3]{-1} \text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (-(-1)^{2/3} \text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to 0 y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 \text {$\#$1}^{5/3}}{5 (-c_1)}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},\frac {3 \text {$\#$1}^{5/3}}{5 (-c_1)}\right )}{\left (-\text {$\#$1}^{5/3}+\frac {5 (-c_1)}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1+\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 (-c_1)}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},-\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 (-c_1)}\right )}{\left (\sqrt [3]{-1} \text {$\#$1}^{5/3}+\frac {5}{3} (-1) c_1\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 (-c_1)}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 (-c_1)}\right )}{\left (-(-1)^{2/3} \text {$\#$1}^{5/3}+\frac {5 (-c_1)}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (-\text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1+\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},-\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (\sqrt [3]{-1} \text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},\frac {3}{5},\frac {8}{5},\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (-(-1)^{2/3} \text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] \end{align*}