23.1.8 problem 1(h)

Internal problem ID [4098]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(h)
Date solved : Monday, January 27, 2025 at 08:08:34 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 56

dsolve((x^3+y(x)^3)-x*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \left (3 \ln \left (x \right )+c_{1} \right )^{{1}/{3}} x \\ y \left (x \right ) &= -\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{2} \\ y \left (x \right ) &= \frac {\left (3 \ln \left (x \right )+c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 63

DSolve[(x^3+y[x]^3)-x*y[x]^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \sqrt [3]{3 \log (x)+c_1} \\ y(x)\to -\sqrt [3]{-1} x \sqrt [3]{3 \log (x)+c_1} \\ y(x)\to (-1)^{2/3} x \sqrt [3]{3 \log (x)+c_1} \\ \end{align*}