30.2.11 problem 11

Internal problem ID [7439]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:35:23 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} t +y+1-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=t+y(t)+1-diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.072 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t + y(t) - Derivative(y(t), t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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