Internal problem ID [7434]
Book: Second order enumerated odes
Section: section 1
Problem number: 45.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y {y^{\prime \prime }}^{2}+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 229
dsolve(y(x)*diff(y(x),x$2)^2+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} y \left (x \right ) = 0 \int _{}^{y \left (x \right )}-\frac {\textit {\_a}}{\left (c_{1} \textit {\_a}^{\frac {3}{2}}-3 \textit {\_a}^{2}\right )^{\frac {2}{3}}}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}-\frac {\textit {\_a}}{\left (c_{1} \textit {\_a}^{\frac {3}{2}}+3 \textit {\_a}^{2}\right )^{\frac {2}{3}}}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}-\frac {4 \textit {\_a}}{\left (c_{1} \textit {\_a}^{\frac {3}{2}}-3 \textit {\_a}^{2}\right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}-\frac {4 \textit {\_a}}{\left (c_{1} \textit {\_a}^{\frac {3}{2}}-3 \textit {\_a}^{2}\right )^{\frac {2}{3}} \left (i \sqrt {3}-1\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}-\frac {4 \textit {\_a}}{\left (c_{1} \textit {\_a}^{\frac {3}{2}}+3 \textit {\_a}^{2}\right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \int _{}^{y \left (x \right )}-\frac {4 \textit {\_a}}{\left (c_{1} \textit {\_a}^{\frac {3}{2}}+3 \textit {\_a}^{2}\right )^{\frac {2}{3}} \left (i \sqrt {3}-1\right )^{2}}d \textit {\_a} -x -c_{2} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 61.116 (sec). Leaf size: 23861
DSolve[y[x]*y''[x]^2+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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