74.7.13 problem 13

Internal problem ID [16090]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 08:39:14 AM
CAS classification : [_separable]

\begin{align*} 2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.326 (sec). Leaf size: 59

dsolve(( 2*ln(t))-( ln(4*y(t)^2) )*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \frac {t \ln \left (t \right )+c_{1} -t}{\operatorname {LambertW}\left (-2 \left (t \ln \left (t \right )+c_{1} -t \right ) {\mathrm e}^{-1}\right )} \\ y &= \frac {t \ln \left (t \right )+c_{1} -t}{\operatorname {LambertW}\left (2 \left (t \ln \left (t \right )+c_{1} -t \right ) {\mathrm e}^{-1}\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.068 (sec). Leaf size: 76

DSolve[( 2*Log[t])-( Log[4*y[t]^2] )*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {-2 t+2 t \log (t)+c_1}{2 W\left (-\frac {-2 t+2 t \log (t)+c_1}{e}\right )} \\ y(t)\to \frac {-2 t+2 t \log (t)+c_1}{2 W\left (\frac {-2 t+2 t \log (t)+c_1}{e}\right )} \\ \end{align*}