Internal problem ID [4434]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{\frac {1}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
dsolve(diff(y(x),x)=y(x)^(1/3),y(x), singsol=all)
\[ y \relax (x )^{\frac {2}{3}}-\frac {2 x}{3}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 29
DSolve[y'[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*}