60.1.200 problem 204

Internal problem ID [10214]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 204
Date solved : Sunday, March 30, 2025 at 03:31:42 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.065 (sec). Leaf size: 56

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

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{\operatorname {RootOf}\left (x^{2} \left (4 \,{\mathrm e}^{\textit {\_Z}} {\cosh \left (\frac {\sqrt {a^{2}-4}\, \left (2 c_1 +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 a}\right )}^{2}+a^{2}-4\right )\right )}+1+\textit {\_Z} a \right ) x \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 38

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]}{K[1]^2+a K[1]+1}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded