Internal problem ID [6684]
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]]
Solve \begin {gather*} \boxed {y \left (y^{\prime \prime }\right )^{3}+y^{3} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.182 (sec). Leaf size: 126
dsolve(y(x)*diff(y(x),x$2)^3+y(x)^3*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = c_{1} \\ y \relax (x ) = {\mathrm e}^{\int \RootOf \left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{-\textit {\_f}^{2}+\left (-\textit {\_f} \right )^{\frac {1}{3}}}d \textit {\_f} \right )+c_{1}\right )d x +c_{2}} \\ y \relax (x ) = {\mathrm e}^{\int \RootOf \left (x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{i \left (-\textit {\_f} \right )^{\frac {1}{3}} \sqrt {3}+2 \textit {\_f}^{2}+\left (-\textit {\_f} \right )^{\frac {1}{3}}}d \textit {\_f} \right )+c_{1}\right )d x +c_{2}} \\ y \relax (x ) = {\mathrm e}^{\int \RootOf \left (x -2 \left (\int _{}^{\textit {\_Z}}\frac {1}{i \left (-\textit {\_f} \right )^{\frac {1}{3}} \sqrt {3}-2 \textit {\_f}^{2}-\left (-\textit {\_f} \right )^{\frac {1}{3}}}d \textit {\_f} \right )+c_{1}\right )d x +c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.741 (sec). Leaf size: 263
DSolve[y[x]*y''[x]^3+y[x]^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \, _2F_1\left (\frac {3}{5},\frac {3}{5};\frac {8}{5};\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (-\text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] \\ y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1+\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \, _2F_1\left (\frac {3}{5},\frac {3}{5};\frac {8}{5};-\frac {3 \sqrt [3]{-1} \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (\sqrt [3]{-1} \text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] \\ y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 c_1}\right ){}^{3/5} \, _2F_1\left (\frac {3}{5},\frac {3}{5};\frac {8}{5};\frac {3 (-1)^{2/3} \text {$\#$1}^{5/3}}{5 c_1}\right )}{\left (-(-1)^{2/3} \text {$\#$1}^{5/3}+\frac {5 c_1}{3}\right ){}^{3/5}}\&\right ][x+c_2] \\ \end{align*}