68.3.4 problem 3

Internal problem ID [17151]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 3
Date solved : Thursday, October 02, 2025 at 01:45:10 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{{1}/{5}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

ode:=diff(y(t),t) = y(t)^(1/5); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 24

ode=D[y[t],t]==y[t]^(1/5); 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {4 \sqrt {2} t^{5/4}}{5 \sqrt [4]{5}} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**(1/5) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out