Internal problem ID [6680]
Book: Second order enumerated odes
Section: section 1
Problem number: 47.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime \prime }\right )^{2}+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 205
dsolve(y(x)^2*diff(y(x),x$2)^2+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} \\ y \relax (x ) = 0 \\ \int _{}^{y \relax (x )}-\frac {4}{\left (-12 \ln \left (\textit {\_a} \right )+8 c_{1}\right )^{\frac {2}{3}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {4}{\left (12 \ln \left (\textit {\_a} \right )-8 c_{1}\right )^{\frac {2}{3}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {16}{\left (-12 \ln \left (\textit {\_a} \right )+8 c_{1}\right )^{\frac {2}{3}} \left (-1+i \sqrt {3}\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {16}{\left (-12 \ln \left (\textit {\_a} \right )+8 c_{1}\right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {16}{\left (12 \ln \left (\textit {\_a} \right )-8 c_{1}\right )^{\frac {2}{3}} \left (-1+i \sqrt {3}\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {16}{\left (12 \ln \left (\textit {\_a} \right )-8 c_{1}\right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.691 (sec). Leaf size: 145
DSolve[y[x]^2*y''[x]^2+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\left (\frac {2}{3}\right )^{2/3} e^{-i c_1} (-\log (\text {$\#$1})-i c_1){}^{2/3} \text {Gamma}\left (\frac {1}{3},-\log (\text {$\#$1})-i c_1\right )}{(c_1-i \log (\text {$\#$1})){}^{2/3}}\&\right ][x+c_2] \\ y(x)\to \text {InverseFunction}\left [\frac {\left (\frac {2}{3}\right )^{2/3} e^{i c_1} (-\log (\text {$\#$1})+i c_1){}^{2/3} \text {Gamma}\left (\frac {1}{3},-\log (\text {$\#$1})+i c_1\right )}{(i \log (\text {$\#$1})+c_1){}^{2/3}}\&\right ][x+c_2] \\ \end{align*}