76.2.7 problem 7

Internal problem ID [17272]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 7
Date solved : Monday, March 31, 2025 at 03:48:15 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 t y&=16 t \,{\mathrm e}^{-t^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(y(t),t)+2*t*y(t) = 16*t*exp(-t^2); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (8 t^{2}+c_1 \right ) {\mathrm e}^{-t^{2}} \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 21

ode=D[y[t],t]+2*t*y[t]==16*t*Exp[-t^2]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t^2} \left (8 t^2+c_1\right ) \]

✓ Sympy. Time used: 0.227 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t*y(t) - 16*t*exp(-t**2) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + 8 t^{2}\right ) e^{- t^{2}} \]