74.4.47 problem 47

Internal problem ID [15940]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 47
Date solved : Tuesday, January 28, 2025 at 08:23:55 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{y+1} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.154 (sec). Leaf size: 16

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

\[ y = -1-\sqrt {2 \,{\mathrm e}^{t}-1} \]

✓ Solution by Mathematica

Time used: 0.550 (sec). Leaf size: 20

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

\[ y(t)\to -\sqrt {2 e^t-1}-1 \]