60.1.100 problem 102

Internal problem ID [10114]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 102
Date solved : Wednesday, March 05, 2025 at 08:31:25 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

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

\[ y = \tanh \left (\sqrt {a}\, \left (\frac {x^{2}}{2}+c_{1} \right )\right ) x \sqrt {a} \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 36

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

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

✗ Sympy

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

Timed Out