80.2.8 problem 10

Internal problem ID [21151]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 2. Theory of first order differential equations. Excercise 2.6 at page 37
Problem number : 10
Date solved : Thursday, October 02, 2025 at 07:10:29 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=x^{p} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(x(t),t) = x(t)^p; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (-t p +c_1 +t \right )^{-\frac {1}{p -1}} \]

✓ Mathematica. Time used: 0.472 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.189 (sec). Leaf size: 29

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

\[ \left [ x{\left (t \right )} = \begin {cases} \left (- C_{1} p + C_{1} - p t + t\right )^{- \frac {1}{p - 1}} & \text {for}\: p \neq 1 \\\text {NaN} & \text {otherwise} \end {cases}, \ x{\left (t \right )} = \begin {cases} C_{1} e^{t} & \text {for}\: p = 1 \\\text {NaN} & \text {otherwise} \end {cases}\right ] \]