56.1.64 problem 64

Internal problem ID [8776]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 64
Date solved : Tuesday, January 28, 2025 at 03:16:46 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 106

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

\[ y = \operatorname {RootOf}\left (\ln \left (x \right )+2^{{1}/{3}} \left (\int _{}^{\textit {\_Z}}\frac {1}{2^{{1}/{3}} \textit {\_f} +2 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right )+\operatorname {AiryBi}\left (1, \frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right ) c_{1} +\operatorname {AiryAi}\left (1, \frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right )\right )}d \textit {\_f} \right )-c_{2} \right ) x \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved