75.21.10 problem 705

Internal problem ID [17179]
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 : Tuesday, January 28, 2025 at 09:56:15 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Solution by Maple

dsolve(diff(x(t),t$2)-diff(x(t),t)+x(t)-x(t)^2=0,x(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved