33.1.5 problem problem 146

Internal problem ID [6023]
Book : Differential Gleichungen, Kamke, 3rd ed, Abel ODEs
Section : Abel ODE with constant invariant
Problem number : problem 146
Date solved : Sunday, March 30, 2025 at 10:32:35 AM
CAS classification : [_rational, _Abel]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 65

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

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

✓ Mathematica. Time used: 0.601 (sec). Leaf size: 78

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded