68.5.4 problem 4

Internal problem ID [17255]
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 : 4
Date solved : Thursday, October 02, 2025 at 02:00:00 PM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to -t^2+c_1 e^t \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 10

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

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