Internal problem ID [13424]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x -2 y^{2}+6 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)=2*y(x)^2-6*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3}{3 c_{1} x^{6}+1} \]
✓ Solution by Mathematica
Time used: 1.886 (sec). Leaf size: 31
DSolve[x*y'[x]==2*y[x]^2-6*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3}{1+e^{3 c_1} x^6} \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}