72.2.6 problem 6

Internal problem ID [14562]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 6
Date solved : Thursday, March 13, 2025 at 03:34:17 AM
CAS classification : [[_linear, `class A`]]

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

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

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

\[ y = -t -2+c_{1} {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.111 (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)
 

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