Internal problem ID [33]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {y^{\prime }-4 \left (y x \right )^{\frac {1}{3}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 91
dsolve(diff(y(x),x) = 4*(x*y(x))^(1/3),y(x), singsol=all)
\[ -\frac {32 x \left (\left (-c_{1} x^{5}+\frac {y \left (x \right )^{2} c_{1} x}{8}+\frac {x}{16}\right ) \left (x y \left (x \right )\right )^{\frac {2}{3}}+\left (c_{1} x^{4}-\frac {y \left (x \right )^{2} c_{1}}{8}+\frac {1}{8}\right ) \left (x^{3}+\frac {y \left (x \right ) \left (x y \left (x \right )\right )^{\frac {1}{3}}}{4}\right )\right )}{\left (8 x^{4}-y \left (x \right )^{2}\right ) \left (-\left (x y \left (x \right )\right )^{\frac {2}{3}}+2 x^{2}\right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 4.813 (sec). Leaf size: 35
DSolve[y'[x] == 4*(x*y[x])^(1/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{3} \sqrt {\frac {2}{3}} \left (3 x^{4/3}+c_1\right ){}^{3/2} \\ y(x)\to 0 \\ \end{align*}