71.8.25 problem 9 (d)

Internal problem ID [14459]
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 (d)
Date solved : Tuesday, January 28, 2025 at 06:36:20 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 19

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

\begin{align*} y(x)\to 0 \\ y(x)\to \left (x^2-1\right )^{3/2} \\ \end{align*}