Internal problem ID [13411]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.4 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact]
\[ \boxed {\ln \left (y x \right )=-1-\frac {x y^{\prime }}{y}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve(1+ln(x*y(x))+x/y(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {c_{1}}{x}}}{x} \]
✓ Solution by Mathematica
Time used: 0.171 (sec). Leaf size: 17
DSolve[1+Log[x*y[x]]+x/y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{\frac {c_1}{x}}}{x} \]