68.5.49 problem 56

Internal problem ID [17300]
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 : 56
Date solved : Thursday, October 02, 2025 at 02:01:11 PM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 33

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

\begin{align*} y(t)&\to e^{3 t} \left (\int _1^t27 e^{-3 K[1]} K[1]^2dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.073 (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),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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