75.21.10 problem 705

Internal problem ID [17108]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 16. The method of isoclines for differential equations of the second order. Exercises page 158
Problem number : 705
Date solved : Monday, March 31, 2025 at 03:41:57 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)-diff(x(t),t)+x(t)-x(t)^2 = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]-D[x[t],t]+x[t]-x[t]^2==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE x(t)**2 - x(t) + Derivative(x(t), t) - Derivative(x(t), (t, 2)) cannot be solved by the factorable group method