60.2.48 problem 624

Internal problem ID [10622]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 624
Date solved : Sunday, March 30, 2025 at 06:11:10 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \end{align*}

✓ Maple. Time used: 0.273 (sec). Leaf size: 46

ode:=diff(y(x),x) = x^(5/3)/(y(x)+x^(4/3)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{192}+12 x^{{4}/{3}} \textit {\_Z}^{176}+48 x^{{8}/{3}} \textit {\_Z}^{160}+64 x^{4} \textit {\_Z}^{144}-c_1 \right )^{16}}{2}+\frac {x^{{4}/{3}}}{2} \]

✓ Mathematica. Time used: 76.14 (sec). Leaf size: 9837

ode=D[y[x],x] == x^(5/3)/(x^(4/3) + y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**(5/3)/(x**(4/3) + y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x**(5/3)/(x**(4/3) + y(x)) + Derivative(y(x), x) cannot be solved by the lie group method