7.2.11 problem 13

Internal problem ID [29]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 13
Date solved : Friday, February 07, 2025 at 08:12:12 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 18

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

\[ y = \frac {\left (2 x +3\right ) \sqrt {6 x +9}}{9} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 23

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

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