Internal problem ID [6690]
Book: Second order enumerated odes
Section: section 2
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime } y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 70
dsolve(diff(y(x),x$2)*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = {\mathrm e}^{\frac {\sqrt {3}\, \left (\int \tan \left (\RootOf \left (-\sqrt {3}\, \ln \left (\frac {4}{3 \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )}\right )-2 \sqrt {3}\, \ln \left (\frac {3}{2}+\frac {\sqrt {3}\, \tan \left (\textit {\_Z} \right )}{2}\right )+6 \sqrt {3}\, c_{1}+6 \sqrt {3}\, x +6 \textit {\_Z} \right )\right )d x \right )}{2}+c_{2}+\frac {x}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 179
DSolve[y''[x]*y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2}{\sqrt [3]{1+\text {InverseFunction}\left [\frac {1}{6} \log \left (\text {$\#$1}^2-\text {$\#$1}+1\right )+\frac {\text {ArcTan}\left (\frac {2 \text {$\#$1}-1}{\sqrt {3}}\right )}{\sqrt {3}}-\frac {1}{3} \log (\text {$\#$1}+1)\&\right ][-x+c_1]} \sqrt [3]{1+\left (-1+\text {InverseFunction}\left [\frac {1}{6} \log \left (\text {$\#$1}^2-\text {$\#$1}+1\right )+\frac {\text {ArcTan}\left (\frac {2 \text {$\#$1}-1}{\sqrt {3}}\right )}{\sqrt {3}}-\frac {1}{3} \log (\text {$\#$1}+1)\&\right ][-x+c_1]\right ) \text {InverseFunction}\left [\frac {1}{6} \log \left (\text {$\#$1}^2-\text {$\#$1}+1\right )+\frac {\text {ArcTan}\left (\frac {2 \text {$\#$1}-1}{\sqrt {3}}\right )}{\sqrt {3}}-\frac {1}{3} \log (\text {$\#$1}+1)\&\right ][-x+c_1]}} \\ \end{align*}