71.4.10 problem 10

Internal problem ID [14382]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:28:55 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 87

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

\[ -\frac {x \left (\left (-4 c_{1} x^{5}+32 y^{2} c_{1} x +2 x \right ) \left (x y\right )^{{2}/{3}}+\left (x^{3}+4 y \left (x y\right )^{{1}/{3}}\right ) \left (c_{1} x^{4}-8 y^{2} c_{1} +1\right )\right )}{\left (x^{4}-8 y^{2}\right ) \left (-2 \left (x y\right )^{{2}/{3}}+x^{2}\right )^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 4.811 (sec). Leaf size: 35

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

\begin{align*} y(x)\to \frac {\left (3 x^{4/3}+4 c_1\right ){}^{3/2}}{6 \sqrt {6}} \\ y(x)\to 0 \\ \end{align*}