Internal problem ID [13432]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{3}+y^{\prime } x y^{2}=-x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
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 ) &= \frac {\left (-4 x^{6}+8 c_{1} \right )^{\frac {1}{3}}}{2 x} \\ y \left (x \right ) &= -\frac {\left (-4 x^{6}+8 c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y \left (x \right ) &= \frac {\left (-4 x^{6}+8 c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 80
DSolve[x^3+y[x]^3+x*y[x]^2*y'[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*}