58.2.48 problem 48

Internal problem ID [9171]
Book : Second order enumerated odes
Section : section 2
Problem number : 48
Date solved : Monday, January 27, 2025 at 05:51:40 PM
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: 0.001 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

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

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

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