9.7.18 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 : Tuesday, September 30, 2025 at 06:15:13 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*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 8

ode:=diff(y(t),t)+y(t) = y(t)^2*exp(-t); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 10

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

\begin{align*} y(t)&\to 2 e^t \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**2*exp(-t) + y(t) + Derivative(y(t), t),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{t} \]