1.64 problem 64

Internal problem ID [7756]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 64
Date solved : Tuesday, October 22, 2024 at 02:29:50 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solve

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

1.64.1 Maple step by step solution

1.64.2 Maple trace

Methods for second order ODEs:
 

1.64.3 Maple dsolve solution

Solving time : 0.101 (sec)
Leaf size : 106

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

\[ y = \operatorname {RootOf}\left (\ln \left (x \right )+2^{{1}/{3}} \left (\int _{}^{\textit {\_Z}}\frac {1}{2^{{1}/{3}} \textit {\_f} +2 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right ) c_1 \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right )+\operatorname {AiryBi}\left (1, \frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right ) c_1 +\operatorname {AiryAi}\left (1, \frac {2 \textit {\_Z}^{2} \textit {\_f} +2^{{2}/{3}}}{2 \textit {\_f}}\right )\right )}d \textit {\_f} \right )-c_2 \right ) x \]

1.64.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

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

Not solved