Internal problem ID [14356]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\ln \left (4 y^{2}\right ) y^{\prime }=-2 \ln \left (t \right )} \]
✓ Solution by Maple
Time used: 0.172 (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 \left (t \right ) &= \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 \left (t \right ) &= \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: 60.066 (sec). Leaf size: 76
DSolve[( 2*Log[t])-( Log[4*y[t]^2] )*y'[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*}