Internal problem ID [13119]
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: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {1}{x y-3 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x)=1/(x*y(x)-3*x),y(x), singsol=all)
\begin{align*} y = 3-\sqrt {9+2 \ln \left (x \right )+2 c_{1}} y = 3+\sqrt {9+2 \ln \left (x \right )+2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 43
DSolve[y'[x]==1/(x*y[x]-3*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3-\sqrt {2 \log (x)+9+2 c_1} y(x)\to 3+\sqrt {2 \log (x)+9+2 c_1} \end{align*}