14.1.6 problem 6

Internal problem ID [2477]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 6
Date solved : Sunday, March 30, 2025 at 12:02:38 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = 1+{\mathrm e}^{-\frac {t^{3}}{3}} c_1 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 24

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

\begin{align*} y(t)\to 1+c_1 e^{-\frac {t^3}{3}} \\ y(t)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.466 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = C_{1} e^{- \frac {t^{3}}{3}} + 1 \]