54.2.400 problem 979

Internal problem ID [12274]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 979
Date solved : Wednesday, October 01, 2025 at 01:26:47 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Abel]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 49

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

\begin{align*} y &= \frac {x \sqrt {c_1 -2 \ln \left (x \right )}-1}{\sqrt {c_1 -2 \ln \left (x \right )}} \\ y &= \frac {x \sqrt {c_1 -2 \ln \left (x \right )}+1}{\sqrt {c_1 -2 \ln \left (x \right )}} \\ \end{align*}

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to x-\frac {1}{\sqrt {-2 \log (x)+c_1}}\\ y(x)&\to x+\frac {1}{\sqrt {-2 \log (x)+c_1}}\\ y(x)&\to x \end{align*}

✓ Sympy. Time used: 0.950 (sec). Leaf size: 61

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

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