8.2.12 problem 14

Internal problem ID [672]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:57:09 AM
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]
 

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