11.6.5 problem 1.2-1 (e)

Internal problem ID [3442]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (e)
Date solved : Tuesday, September 30, 2025 at 06:38:29 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(y(t),t) = -y(t)+t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = t -1+{\mathrm e}^{-t} c_1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to t+c_1 e^{-t}-1 \end{align*}

✓ Sympy. Time used: 0.069 (sec). Leaf size: 10

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

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