74.6.39 problem 40

Internal problem ID [16062]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 08:34:09 AM
CAS classification : [_exact]

\begin{align*} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✗ Solution by Maple

dsolve([(2*t/(1+t^2)+y(t))+(exp(y(t))+t)*diff(y(t),t)=0,y(0) = 0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{(2*t/(1+t^2)+y[t])+(Exp[y[t]]+t)*D[y[t],t]==0,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

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