72.5.24 problem 11

Internal problem ID [14710]
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
Date solved : Tuesday, January 28, 2025 at 07:12:17 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \ln \left ({| y|}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.274 (sec). Leaf size: 21

dsolve(diff(y(t),t)=y(t)*ln(abs(y(t))),y(t), singsol=all)
 

\begin{align*} y &= {\mathrm e}^{-c_{1} {\mathrm e}^{t}} \\ y &= -{\mathrm e}^{-c_{1} {\mathrm e}^{t}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 35

DSolve[D[y[t],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*}