Internal problem ID [7441]
Book: Second order enumerated odes
Section: section 1
Problem number: 52.
ODE order: 2.
ODE degree: 3.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 248
dsolve(y(x)*diff(y(x),x$2)^3+y(x)^3*diff(y(x),x)^5=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = c_{1} \int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (-5 \left (\int _{\textit {\_g}}^{\textit {\_Z}}\frac {1}{-\textit {\_a} \left (-\textit {\_a}^{2} \textit {\_f}^{2}\right )^{\frac {1}{3}}+5 \textit {\_f}}d \textit {\_f} \right )-\ln \left (\textit {\_a}^{5}+125\right )+5 c_{1} \right )}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (-i \ln \left (\textit {\_a}^{5}+125\right )+\sqrt {3}\, \ln \left (\textit {\_a}^{5}+125\right )+20 \left (\int _{\textit {\_g}}^{\textit {\_Z}}\frac {i \sqrt {3}-1}{\left (5 i \sqrt {3}\, \textit {\_f} -2 \textit {\_a} \left (-\textit {\_a}^{2} \textit {\_f}^{2}\right )^{\frac {1}{3}}-5 \textit {\_f} \right ) \left (\sqrt {3}+i\right )}d \textit {\_f} \right )-20 c_{1} \right )}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (i \ln \left (\textit {\_a}^{5}+125\right )+\sqrt {3}\, \ln \left (\textit {\_a}^{5}+125\right )-20 \left (\int _{\textit {\_g}}^{\textit {\_Z}}-\frac {1+i \sqrt {3}}{\left (5 i \sqrt {3}\, \textit {\_f} +2 \textit {\_a} \left (-\textit {\_a}^{2} \textit {\_f}^{2}\right )^{\frac {1}{3}}+5 \textit {\_f} \right ) \left (-i+\sqrt {3}\right )}d \textit {\_f} \right )+20 c_{1} \right )}d \textit {\_a} -x -c_{2} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 24.581 (sec). Leaf size: 449
DSolve[y[x]*y''[x]^3+y[x]^3*y'[x]^5==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right )}{c_1{}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},-\frac {3 i \left (-i+\sqrt {3}\right ) \text {$\#$1}^{5/3}}{10 c_1}\right )}{c_1{}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},\frac {3 i \left (i+\sqrt {3}\right ) \text {$\#$1}^{5/3}}{10 c_1}\right )}{c_1{}^3}\&\right ][x+c_2] y(x)\to 0 y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},\frac {3 \text {$\#$1}^{5/3}}{5 (-c_1)}\right )}{(-c_1){}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},-\frac {3 i \left (-i+\sqrt {3}\right ) \text {$\#$1}^{5/3}}{10 (-c_1)}\right )}{(-c_1){}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},\frac {3 i \left (i+\sqrt {3}\right ) \text {$\#$1}^{5/3}}{10 (-c_1)}\right )}{(-c_1){}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},\frac {3 \text {$\#$1}^{5/3}}{5 c_1}\right )}{c_1{}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},-\frac {3 i \left (-i+\sqrt {3}\right ) \text {$\#$1}^{5/3}}{10 c_1}\right )}{c_1{}^3}\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [\frac {27 \text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {3}{5},3,\frac {8}{5},\frac {3 i \left (i+\sqrt {3}\right ) \text {$\#$1}^{5/3}}{10 c_1}\right )}{c_1{}^3}\&\right ][x+c_2] \end{align*}