58.1.51 problem 51

Internal problem ID [9122]
Book : Second order enumerated odes
Section : section 1
Problem number : 51
Date solved : Wednesday, March 05, 2025 at 07:26:17 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.184 (sec). Leaf size: 126

ode:=y(x)*diff(diff(y(x),x),x)^3+y(x)^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= c_{1} \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (x -\int _{}^{\textit {\_Z}}-\frac {1}{\textit {\_f}^{2}-\left (-\textit {\_f} \right )^{{1}/{3}}}d \textit {\_f} +c_{1} \right )d x +c_{2}} \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{i \left (-\textit {\_f} \right )^{{1}/{3}} \sqrt {3}+2 \textit {\_f}^{2}+\left (-\textit {\_f} \right )^{{1}/{3}}}d \textit {\_f} \right )+c_{1} \right )d x +c_{2}} \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (x -2 \left (\int _{}^{\textit {\_Z}}\frac {1}{i \left (-\textit {\_f} \right )^{{1}/{3}} \sqrt {3}-2 \textit {\_f}^{2}-\left (-\textit {\_f} \right )^{{1}/{3}}}d \textit {\_f} \right )+c_{1} \right )d x +c_{2}} \\ \end{align*}

✓ Mathematica. Time used: 2.742 (sec). Leaf size: 800

ode=y[x]*D[y[x],{x,2}]^3+y[x]^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.253 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**3*Derivative(y(x), x) + y(x)*Derivative(y(x), (x, 2))**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 0 \]