Internal problem ID [14429]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Bernoulli]
\[ \boxed {y-y^{\prime } t -2 y^{2} \ln \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(y(t)-t*diff(y(t),t)=2*y(t)^2*ln(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {t}{2 t \ln \left (t \right )-2 t +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 25
DSolve[y[t]-t*y'[t]==2*y[t]^2*Log[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t}{-2 t+2 t \log (t)+c_1} \\ y(t)\to 0 \\ \end{align*}