68.5.34 problem 34

Internal problem ID [17285]
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 : 34
Date solved : Thursday, October 02, 2025 at 02:00:54 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} x \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

ode:=diff(x(t),t) = x(t)+t+1; 
ic:=[x(0) = 2]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -t -2+4 \,{\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 29

ode=D[x[t],t]==x[t]+t+1; 
ic={x[0]==2}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^t \left (\int _0^te^{-K[1]} (K[1]+1)dK[1]+2\right ) \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t - x(t) + Derivative(x(t), t) - 1,0) 
ics = {x(0): 2} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - t + 4 e^{t} - 2 \]