54.2.221 problem 798

Internal problem ID [12095]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 798
Date solved : Wednesday, October 01, 2025 at 12:32:07 AM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 30

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}+\ln \left (x +1\right ) {\mathrm e}^{\textit {\_Z}}+c_1 \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]

✓ Mathematica. Time used: 0.265 (sec). Leaf size: 65

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

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

✗ Sympy

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

Timed Out