Internal problem ID [14394]
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: 54.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } t -\ln \left (y^{\prime }\right )=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(1+y(t)-t*diff(y(t),t)=ln(diff(y(t),t)),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \ln \left (-\frac {1}{t}\right )-2 \\ y \left (t \right ) &= -1+c_{1} t +\ln \left (c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 26
DSolve[1+y[t]-t*y'[t]==Log[y'[t]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 t-1+\log (c_1) \\ y(t)\to \log \left (-\frac {1}{t}\right )-2 \\ \end{align*}