69.21.5 problem 700

Internal problem ID [18461]
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 : 700
Date solved : Thursday, October 02, 2025 at 03:12:21 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(-16*x(t) + 8*Derivative(x(t), (t, 2)) + 1)/4 + Derivative(x(t), t) - 1/4 cannot be solved by the factorable group method