71.8.24 problem 9 (c)

Internal problem ID [14458]
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 (c)
Date solved : Tuesday, January 28, 2025 at 06:34:24 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.536 (sec). Leaf size: 30

dsolve([diff(y(x),x)=3*x*y(x)^(1/3),y(-1) = 1/2],y(x), singsol=all)
 

\[ y = \frac {\sqrt {4 x^{2}+2 \,2^{{1}/{3}}-4}\, \left (2 x^{2}+2^{{1}/{3}}-2\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 30

DSolve[{D[y[x],x]==3*x*y[x]^(1/3),{y[-1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

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