60.1.109 problem 111

Internal problem ID [10123]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 111
Date solved : Sunday, March 30, 2025 at 03:17:13 PM
CAS classification : [_rational, _Abel]

\begin{align*} x y^{\prime }+y^{3}+3 x y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 57

ode:=x*diff(y(x),x)+y(x)^3+3*x*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {3 \,\operatorname {erf}\left (\frac {i \left (3 y x -1\right ) \sqrt {2}}{2 y}\right ) \sqrt {2}\, \sqrt {\pi }\, x -2 i {\mathrm e}^{\frac {\left (3 y x -1\right )^{2}}{2 y^{2}}}+6 c_1 x}{6 x} = 0 \]

✓ Mathematica. Time used: 0.327 (sec). Leaf size: 55

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

\[ \text {Solve}\left [-3 x=\frac {2 e^{\frac {1}{2} \left (\frac {1}{y(x)}-3 x\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {\frac {1}{y(x)}-3 x}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded