Internal problem ID [13435]
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: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {3 y^{3} x -y+y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(3*x*y(x)^3-y(x)+x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x}{\sqrt {2 x^{3}+c_{1}}} \\ y \left (x \right ) &= -\frac {x}{\sqrt {2 x^{3}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 43
DSolve[3*x*y[x]^3-y[x]+x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {2 x^3+c_1}} \\ y(x)\to \frac {x}{\sqrt {2 x^3+c_1}} \\ y(x)\to 0 \\ \end{align*}