10.1.12 problem 12

Internal problem ID [1109]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 12
Date solved : Tuesday, March 04, 2025 at 12:09:18 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=y(t)+2*diff(y(t),t) = 3*t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = 3 t^{2}-12 t +24+{\mathrm e}^{-\frac {t}{2}} c_1 \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 25

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

\[ y(t)\to 3 t^2-12 t+c_1 e^{-t/2}+24 \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = C_{1} e^{- \frac {t}{2}} + 3 t^{2} - 12 t + 24 \]