74.3.4 problem 3

Internal problem ID [15864]
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 : Tuesday, January 28, 2025 at 08:10:35 AM
CAS classification : [_quadrature]

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

With initial conditions

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(t),t)=y(t)^(1/5),y(0) = 0],y(t), singsol=all)
 
\[ y = 0 \]

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 24

DSolve[{D[y[t],t]==y[t]^(1/5),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 
\[ y(t)\to \frac {4 \sqrt {2} t^{5/4}}{5 \sqrt [4]{5}} \]