63.5.36 problem 16-b(v)

Internal problem ID [13039]
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 : 16-b(v)
Date solved : Monday, March 31, 2025 at 07:32:28 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ x = \frac {t}{c_1 t +1} \]

✓ Mathematica. Time used: 0.123 (sec). Leaf size: 21

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

\begin{align*} x(t)\to \frac {t}{1-c_1 t} \\ x(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 10

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

\[ x{\left (t \right )} = - \frac {t}{C_{1} t - 1} \]