63.5.5 problem 1(e)

Internal problem ID [13008]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 1(e)
Date solved : Monday, March 31, 2025 at 07:30:36 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x x^{\prime }&=1-t x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 47

ode:=x(t)*diff(x(t),t) = 1-t*x(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {\left (2^{{2}/{3}} t^{2}-4 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\textit {\_Z} \right ) 2^{{1}/{3}} c_1 t +2^{{1}/{3}} t \operatorname {AiryAi}\left (\textit {\_Z} \right )-2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_1 -2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right )\right ) 2^{{1}/{3}}}{4} \]

✓ Mathematica. Time used: 0.201 (sec). Leaf size: 121

ode=x[t]*D[x[t],t]==1-t*x[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {(-1)^{2/3} \sqrt [3]{2} t \operatorname {AiryAi}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (t^2+2 x(t)\right )\right )-2 \operatorname {AiryAiPrime}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (t^2+2 x(t)\right )\right )}{(-1)^{2/3} \sqrt [3]{2} t \operatorname {AiryBi}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (t^2+2 x(t)\right )\right )-2 \operatorname {AiryBiPrime}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (t^2+2 x(t)\right )\right )}+c_1=0,x(t)\right ] \]

✗ Sympy

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

NotImplementedError : The given ODE t + Derivative(x(t), t) - 1/x(t) cannot be solved by the factorable group method