68.5.45 problem 52

Internal problem ID [17296]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 52
Date solved : Thursday, October 02, 2025 at 02:01:05 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 3 y+y^{\prime }&=27 t^{2}+9 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(t),t)+3*y(t) = 27*t^2+9; 
dsolve(ode,y(t), singsol=all);
 

\[ y = 9 t^{2}-6 t +5+{\mathrm e}^{-3 t} c_1 \]

✓ Mathematica. Time used: 0.116 (sec). Leaf size: 37

ode=D[y[t],t]+3*y[t]==27*t^2+9; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-3 t} \left (\int _1^t9 e^{3 K[1]} \left (3 K[1]^2+1\right )dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-27*t**2 + 3*y(t) + Derivative(y(t), t) - 9,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 3 t} + 9 t^{2} - 6 t + 5 \]