10.1.19 problem 19

Internal problem ID [1116]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 19
Date solved : Saturday, March 29, 2025 at 10:39:33 PM
CAS classification : [_linear]

\begin{align*} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 16

ode:=4*t^2*y(t)+t^3*diff(y(t),t) = exp(-t); 
ic:=y(-1) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {\left (t +1\right ) {\mathrm e}^{-t}}{t^{4}} \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 18

ode=4*t^2*y[t]+t^3*D[y[t],t] == Exp[-t]; 
ic=y[-1]==0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {e^{-t} (t+1)}{t^4} \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**3*Derivative(y(t), t) + 4*t**2*y(t) - exp(-t),0) 
ics = {y(-1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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