60.1.179 problem 182

Internal problem ID [10193]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 182
Date solved : Sunday, March 30, 2025 at 03:28:23 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=x*(x^3-1)*diff(y(x),x)-2*x*y(x)^2+y(x)+x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x \left (c_1 +x \right )}{c_1 \,x^{2}+1} \]

✓ Mathematica. Time used: 0.715 (sec). Leaf size: 31

ode=x*(x^3-1)*D[y[x],x] - 2*x*y[x]^2 + y[x] + x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {x (1+2 c_1 x)}{x^2+2 c_1} \\ y(x)\to x^2 \\ \end{align*}

✓ Sympy. Time used: 0.343 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + x*(x**3 - 1)*Derivative(y(x), x) - 2*x*y(x)**2 + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \left (C_{1} x - x + 1\right )}{C_{1} + x^{2} - 1} \]