13.2.6 problem 6

Internal problem ID [2304]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 6
Date solved : Saturday, March 29, 2025 at 11:53:24 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 24

ode=t^2*y[t]+D[y[t],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: 0.328 (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)
 

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