58.1.45 problem 45

Internal problem ID [9116]
Book : Second order enumerated odes
Section : section 1
Problem number : 45
Date solved : Monday, January 27, 2025 at 05:42:28 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.100 (sec). Leaf size: 263

dsolve(y(x)*diff(y(x),x$2)^2+diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= c_{1} \\ y &= 0 \\ -\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} -x -c_{2} &= 0 \\ -\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} -x -c_{2} &= 0 \\ \frac {-4 \left (\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{{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}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{{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}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{{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}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{{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: 61.031 (sec). Leaf size: 23861

DSolve[y[x]*D[y[x],{x,2}]^2+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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