71.8.26 problem 9 (e)

Internal problem ID [14460]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 9 (e)
Date solved : Tuesday, January 28, 2025 at 06:36:30 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 7

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

\[ y = x^{3} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 67

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

\begin{align*} y(x)\to \frac {\left (2 x^2-i \sqrt {3}-3\right )^{3/2}}{2 \sqrt {2}} \\ y(x)\to \frac {\left (2 x^2+i \sqrt {3}-3\right )^{3/2}}{2 \sqrt {2}} \\ \end{align*}