74.5.34 problem 34

Internal problem ID [15998]
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 : Tuesday, January 28, 2025 at 08:26:06 AM
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*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([diff(x(t),t)=x(t)+t+1,x(0) = 2],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 29

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

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