90.3.27 problem 27

Internal problem ID [25091]
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 41
Problem number : 27
Date solved : Thursday, October 02, 2025 at 11:49:53 PM
CAS classification : [_separable]

\begin{align*} 2 y t +y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 12

ode:=diff(y(t),t)+2*t*y(t) = 0; 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 4 \,{\mathrm e}^{-t^{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 14

ode=D[y[t],{t,1}]+2*y[t]*t ==0; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 4 e^{-t^2} \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 4 e^{- t^{2}} \]