73.7.10 problem 10

Internal problem ID [15168]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 07:39:38 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: 0.006 (sec). Leaf size: 72

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

\begin{align*} y &= \frac {\left (-4 x^{6}+8 c_{1} \right )^{{1}/{3}}}{2 x} \\ y &= -\frac {\left (-4 x^{6}+8 c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y &= \frac {\left (-4 x^{6}+8 c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.230 (sec). Leaf size: 80

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 -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{-x^6+2 c_1}}{x} \\ y(x)\to \frac {\sqrt [3]{-\frac {x^6}{2}+c_1}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-\frac {x^6}{2}+c_1}}{x} \\ \end{align*}