Internal problem ID [12654]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y \ln \left ({| y|}\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve(diff(y(t),t)=y(t)*ln(abs(y(t))),y(t), singsol=all)
\begin{align*} y \left (t \right ) = {\mathrm e}^{-c_{1} {\mathrm e}^{t}} y \left (t \right ) = -{\mathrm e}^{-c_{1} {\mathrm e}^{t}} \end{align*}
✓ Solution by Mathematica
Time used: 0.321 (sec). Leaf size: 35
DSolve[y'[t]==y[t]*Log[Abs[y[t]]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] \log (| K[1]| )}dK[1]\&\right ][t+c_1] y(t)\to 1 \end{align*}