74.8.32 problem 32

Internal problem ID [16168]
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 : 32
Date solved : Tuesday, January 28, 2025 at 08:55:35 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.316 (sec). Leaf size: 14

dsolve([(y(t)*exp(t*y(t))-2*t)+(t*exp(t*y(t)))*diff(y(t),t)=0,y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\ln \left (t^{2}+1\right )}{t} \]

✓ Solution by Mathematica

Time used: 0.486 (sec). Leaf size: 15

DSolve[{(y[t]*Exp[t*y[t]]-2*t)+(t*Exp[t*y[t]])*D[y[t],t]==0,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\log \left (t^2+1\right )}{t} \]