60.1.305 problem 311

Internal problem ID [10319]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 311
Date solved : Wednesday, March 05, 2025 at 10:13:03 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \left (20 y^{3}-3 x y^{2}+6 x^{2} y+3 x^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.064 (sec). Leaf size: 50

ode:=(20*y(x)^3-3*x*y(x)^2+6*x^2*y(x)+3*x^3)*diff(y(x),x)-y(x)^3+6*x*y(x)^2+9*x^2*y(x)+4*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (c_{1}^{4} x^{4}+3 \textit {\_Z} \,c_{1}^{3} x^{3}+3 \textit {\_Z}^{2} c_{1}^{2} x^{2}-\textit {\_Z}^{3} c_{1} x +5 \textit {\_Z}^{4}-1\right )}{c_{1}} \]

✓ Mathematica. Time used: 60.182 (sec). Leaf size: 2201

ode=4*x^3 + 9*x^2*y[x] + 6*x*y[x]^2 - y[x]^3 + (3*x^3 + 6*x^2*y[x] - 3*x*y[x]^2 + 20*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

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3 + 9*x**2*y(x) + 6*x*y(x)**2 + (3*x**3 + 6*x**2*y(x) - 3*x*y(x)**2 + 20*y(x)**3)*Derivative(y(x), x) - y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out