80.2.7 problem 9

Internal problem ID [21150]
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 : 9
Date solved : Thursday, October 02, 2025 at 07:10:26 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=x^{{1}/{4}} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=a \\ \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 26

ode:=diff(x(t),t) = x(t)^(1/4); 
ic:=[x(0) = a]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \frac {\left (4 a^{{3}/{4}}+3 t \right ) \left (8 a^{{3}/{4}}+6 t \right )^{{1}/{3}}}{8} \]

✓ Mathematica. Time used: 0.115 (sec). Leaf size: 29

ode=D[x[t],t]==x[t]^(1/4); 
ic={x[0]==a}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {\left (4 a^{3/4}+3 t\right )^{4/3}}{4\ 2^{2/3}} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
x = Function("x") 
ode = Eq(-x(t)**(1/4) + Derivative(x(t), t),0) 
ics = {x(0): a} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants