90.2.6 problem 6

Internal problem ID [25057]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 23
Problem number : 6
Date solved : Thursday, October 02, 2025 at 11:47:59 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(t),t) = -t*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {t^{2}}{2}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 22

ode=D[y[t],{t,1}]== -t*y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{-\frac {t^2}{2}}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = C_{1} e^{- \frac {t^{2}}{2}} \]