72.7.10 problem 10

Internal problem ID [14672]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 10
Date solved : Thursday, March 13, 2025 at 04:13:31 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 16

ode:=diff(y(t),t) = -2*t*y(t)+4*exp(-t^2); 
ic:=y(0) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left (4 t +3\right ) {\mathrm e}^{-t^{2}} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 18

ode=D[y[t],t]==-2*t*y[t]+4*Exp[-t^2]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t^2} (4 t+3) \]

✓ Sympy. Time used: 0.221 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t*y(t) + Derivative(y(t), t) - 4*exp(-t**2),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (4 t + 3\right ) e^{- t^{2}} \]