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]]
Solve \begin {gather*} \boxed {y^{\prime }-4 \left (y x \right )^{\frac {1}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 108
dsolve(diff(y(x),x) = 4*(x*y(x))^(1/3),y(x), singsol=all)
\[ \frac {\left (x y \relax (x )\right )^{\frac {4}{3}}}{\left (-8 x^{4}+y \relax (x )^{2}\right ) \left (\left (x y \relax (x )\right )^{\frac {2}{3}}-2 x^{2}\right )^{2}}+\frac {2 x^{2} \left (x y \relax (x )\right )^{\frac {2}{3}}}{\left (-8 x^{4}+y \relax (x )^{2}\right ) \left (\left (x y \relax (x )\right )^{\frac {2}{3}}-2 x^{2}\right )^{2}}+\frac {4 x^{4}}{\left (-8 x^{4}+y \relax (x )^{2}\right ) \left (\left (x y \relax (x )\right )^{\frac {2}{3}}-2 x^{2}\right )^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.178 (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*}