14.5.4 problem 4

Internal problem ID [2541]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.17. What to do in practice. Excercises page 126
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:59:46 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 8

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

\[ y = {\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 10

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

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