Internal problem ID [7108]
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]]
\[ \boxed {y^{2} y^{\prime \prime }=x} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 106
dsolve(y(x)^2*diff(y(x),x$2)=x,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\ln \left (x \right )+2^{\frac {1}{3}} \left (\int _{}^{\textit {\_Z}}\frac {1}{2^{\frac {1}{3}} \textit {\_f} +2 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{\frac {2}{3}}}{2 \textit {\_f}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{\frac {2}{3}}}{2 \textit {\_f}}\right )+\operatorname {AiryBi}\left (1, \frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{\frac {2}{3}}}{2 \textit {\_f}}\right ) c_{1} +\operatorname {AiryAi}\left (1, \frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{\frac {2}{3}}}{2 \textit {\_f}}\right )\right )}d \textit {\_f} \right )-c_{2} \right ) x \]
✗ 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