7.3.7 problem 7

Internal problem ID [47]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 7
Date solved : Friday, February 07, 2025 at 08:13:04 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 91

dsolve(diff(y(x),x)=(64*x*y(x))^(1/3),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.790 (sec). Leaf size: 35

DSolve[D[y[x],x]==(64*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*}