76.3.13 problem 13

Internal problem ID [17384]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 10:03:57 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{{1}/{3}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 5

dsolve([diff(y(t),t)=y(t)^(1/3),y(0) = 0],y(t), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 21

DSolve[{D[y[t],t]==y[t]^(1/3),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2}{3} \sqrt {\frac {2}{3}} t^{3/2} \]