78.3.10 problem 1 (j)

Internal problem ID [18113]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (j)
Date solved : Tuesday, January 28, 2025 at 11:28:33 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: 0.009 (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 (c_1 +3 \ln \left (x \right )\right )^{{1}/{3}} x \\ y &= -\frac {\left (c_1 +3 \ln \left (x \right )\right )^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{2} \\ y &= \frac {\left (c_1 +3 \ln \left (x \right )\right )^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.179 (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*}