8.2.11 problem 13

Internal problem ID [671]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 13
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 )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 18

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

\[ y = \frac {\left (2 x +3\right ) \sqrt {6 x +9}}{9} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 23

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

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