90.1.22 problem 33

Internal problem ID [25046]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 33
Date solved : Thursday, October 02, 2025 at 11:47:49 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

ode:=diff(y(t),t) = -y(t)+3*t; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 3 t -3+3 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 15

ode=D[y[t],{t,1}]== -y[t]+3*t; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 3 \left (t+e^{-t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 12

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

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