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: 0.078 (sec). Leaf size: 271
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 \\ -\left (\int _{}^{y \left (x \right )}\frac {\textit {\_a}}{\left (\textit {\_a}^{\frac {3}{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{\frac {2}{3}}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ -\left (\int _{}^{y \left (x \right )}\frac {\textit {\_a}}{\left (\textit {\_a}^{\frac {3}{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{\frac {2}{3}}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \frac {-4 \left (\int _{}^{y \left (x \right )}\frac {\textit {\_a}}{\left (\textit {\_a}^{\frac {3}{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{\frac {2}{3}}}d \textit {\_a} \right )+2 i \left (-x -c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (-i \sqrt {3}-1\right )^{2}} &= 0 \\ \frac {-4 \left (\int _{}^{y \left (x \right )}\frac {\textit {\_a}}{\left (\textit {\_a}^{\frac {3}{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{\frac {2}{3}}}d \textit {\_a} \right )+2 i \left (x +c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (1-i \sqrt {3}\right )^{2}} &= 0 \\ \frac {-4 \left (\int _{}^{y \left (x \right )}\frac {\textit {\_a}}{\left (\textit {\_a}^{\frac {3}{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{\frac {2}{3}}}d \textit {\_a} \right )+2 i \left (-x -c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (-i \sqrt {3}-1\right )^{2}} &= 0 \\ \frac {-4 \left (\int _{}^{y \left (x \right )}\frac {\textit {\_a}}{\left (\textit {\_a}^{\frac {3}{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{\frac {2}{3}}}d \textit {\_a} \right )+2 i \left (x +c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (1-i \sqrt {3}\right )^{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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