Internal problem ID [13130]
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: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(ln(y(x))+(x/y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x \operatorname {LambertW}\left (\frac {3 \,{\mathrm e}^{\frac {c_{1}}{x}}}{x}\right )-c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 0.925 (sec). Leaf size: 29
DSolve[Log[y[x]]+(x/y[x]+3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} x W\left (\frac {3 e^{\frac {c_1}{x}}}{x}\right ) y(x)\to 1 \end{align*}