15.7.18 problem 18

Internal problem ID [2999]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 18
Date solved : Monday, January 27, 2025 at 07:07:03 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 10

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

\[ y(t)\to 2 e^t \]