54.2.241 problem 818

Internal problem ID [12115]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 818
Date solved : Wednesday, October 01, 2025 at 12:44:21 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+x y+x y^{3}+x y^{4}\right )} \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 34

ode:=diff(y(x),x) = y(x)/x/(-1+x*y(x)+x*y(x)^3+x*y(x)^4); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-2 x \,{\mathrm e}^{4 \textit {\_Z}}-3 x \,{\mathrm e}^{3 \textit {\_Z}}+6 c_1 x \,{\mathrm e}^{\textit {\_Z}}-6 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}-6\right )} \]

✓ Mathematica. Time used: 0.107 (sec). Leaf size: 34

ode=D[y[x],x] == y[x]/(x*(-1 + x*y[x] + x*y[x]^3 + x*y[x]^4)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)^3}{3}+\frac {y(x)^2}{2}+\frac {1}{x y(x)}+\log (y(x))=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.694 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - y(x)/(x*(x*y(x)**4 + x*y(x)**3 + x*y(x) - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - \frac {y^{3}{\left (x \right )}}{3} - \frac {y^{2}{\left (x \right )}}{2} - \log {\left (y{\left (x \right )} \right )} - \frac {1}{x y{\left (x \right )}} = 0 \]