36.1.31 problem 29 part(a)

Internal problem ID [6286]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 29 part(a)
Date solved : Monday, January 27, 2025 at 01:54:40 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y^{{2}/{3}}-\frac {2 x}{3}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {2}{3} \sqrt {\frac {2}{3}} (x+c_1){}^{3/2} \\ y(x)\to 0 \\ \end{align*}