Internal problem ID [6355]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 64.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{2} y^{\prime \prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 107
dsolve(y(x)^2*diff(y(x),x$2)=x,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\ln \relax (x )-2^{\frac {1}{3}} \left (\int _{}^{\textit {\_Z}}\frac {1}{2^{\frac {1}{3}} \textit {\_f} +2 \RootOf \left (\AiryBi \left (\frac {2 \textit {\_f} \,\textit {\_Z}^{2}+2^{\frac {2}{3}}}{2 \textit {\_f}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \AiryAi \left (\frac {2 \textit {\_f} \,\textit {\_Z}^{2}+2^{\frac {2}{3}}}{2 \textit {\_f}}\right )+\AiryBi \left (1, \frac {2 \textit {\_f} \,\textit {\_Z}^{2}+2^{\frac {2}{3}}}{2 \textit {\_f}}\right ) c_{1}+\AiryAi \left (1, \frac {2 \textit {\_f} \,\textit {\_Z}^{2}+2^{\frac {2}{3}}}{2 \textit {\_f}}\right )\right )}d \textit {\_f} \right )+c_{2}\right ) x \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]^2*y''[x]==x,y[x],x,IncludeSingularSolutions -> True]
Not solved