Internal problem ID [12326]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {y^{\prime }-\left (y x \right )^{\frac {1}{3}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 120
dsolve(diff(y(x),x)=(x*y(x))^(1/3),y(x), singsol=all)
\[ \frac {4 \left (x y \left (x \right )\right )^{\frac {4}{3}}}{\left (-x^{4}+8 y \left (x \right )^{2}\right ) \left (2 \left (x y \left (x \right )\right )^{\frac {2}{3}}-x^{2}\right )^{2}}+\frac {2 x^{2} \left (x y \left (x \right )\right )^{\frac {2}{3}}}{\left (-x^{4}+8 y \left (x \right )^{2}\right ) \left (2 \left (x y \left (x \right )\right )^{\frac {2}{3}}-x^{2}\right )^{2}}+\frac {x^{4}}{\left (-x^{4}+8 y \left (x \right )^{2}\right ) \left (2 \left (x y \left (x \right )\right )^{\frac {2}{3}}-x^{2}\right )^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 4.979 (sec). Leaf size: 35
DSolve[y'[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*}