Internal problem ID [13065]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.5 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {3 y}{x}-\frac {y^{2}}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(diff(y(x),x)-3*y(x)/x=(y(x)/x)^2,y(x), singsol=all)
\[ y = \frac {2 x^{3}}{-x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 25
DSolve[y'[x]-3*y[x]/x==(y[x]/x)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 x^3}{x^2-2 c_1} y(x)\to 0 \end{align*}