54.2.255 problem 832

Internal problem ID [12129]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 832
Date solved : Wednesday, October 01, 2025 at 12:51:43 AM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (y^{4}+y^{3}+y^{2}+x \right ) \left (x +1\right )} \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 31

ode:=diff(y(x),x) = 1/(y(x)^4+y(x)^3+y(x)^2+x)*(x+y(x)+1)*y(x)/(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (x +1\right )+\frac {x}{y}-\frac {y^{3}}{3}-\frac {y^{2}}{2}-y+c_1 = 0 \]

✓ Mathematica. Time used: 0.246 (sec). Leaf size: 64

ode=D[y[x],x] == (y[x]*(1 + x + y[x]))/((1 + x)*(x + y[x]^2 + y[x]^3 + y[x]^4)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ 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 + y(x)**4 + y(x)**3 + y(x)**2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out