56.1.63 problem 63

Internal problem ID [8775]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 63
Date solved : Sunday, March 30, 2025 at 01:32:57 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

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

✗ Maple

ode:=y(x)*diff(diff(y(x),x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + y(x)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -x + y(x)*Derivative(y(x), (x, 2))