Internal problem ID [4435]
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(b).
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*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 5
dsolve([diff(y(x),x)=y(x)^(1/3),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = 0 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{y'[x]==y[x]^(1/3),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{3} \sqrt {\frac {2}{3}} x^{3/2} \\ \end{align*}