8.1.10 problem 10

Internal problem ID [2481]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 05:36:40 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\sqrt {t^{2}+1}\, {\mathrm e}^{-t} y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 5

ode:=diff(y(t),t)+(t^2+1)^(1/2)*exp(-t)*y(t) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 2.171 (sec). Leaf size: 3

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(sqrt(t**2 + 1)*y(t)*exp(-t) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 0 \]