74.7.51 problem 54

Internal problem ID [16128]
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
Date solved : Tuesday, January 28, 2025 at 08:50:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} 1+y-y^{\prime } t&=\ln \left (y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (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 &= \ln \left (-\frac {1}{t}\right )-2 \\ y &= -1+c_{1} t +\ln \left (c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 26

DSolve[1+y[t]-t*D[y[t],t]==Log[D[y[t],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*}