8.3.7 problem 7

Internal problem ID [683]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:57:42 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{\prime }&=4 \left (y x \right )^{{1}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 91

dsolve(diff(y(x),x) = 4*(x*y(x))^(1/3),y(x), singsol=all)
 

\[ -\frac {32 x \left (\left (-c_1 \,x^{5}+\frac {y^{2} c_1 x}{8}+\frac {x}{16}\right ) \left (x y\right )^{{2}/{3}}+\left (x^{3}+\frac {y \left (x y\right )^{{1}/{3}}}{4}\right ) \left (c_1 \,x^{4}-\frac {y^{2} c_1}{8}+\frac {1}{8}\right )\right )}{\left (8 x^{4}-y^{2}\right ) \left (-\left (x y\right )^{{2}/{3}}+2 x^{2}\right )^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 4.806 (sec). Leaf size: 35

DSolve[D[y[x],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*}