74.22.2 problem 2

Internal problem ID [16649]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 09:16:14 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x\\ y^{\prime }\left (t \right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 14

dsolve([diff(x(t),t)=x(t),diff(y(t),t)=1],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t} \\ y &= c_{2} +t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 30

DSolve[{D[x[t],t]==x[t],D[y[t],t]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 e^t \\ y(t)\to t+c_2 \\ x(t)\to 0 \\ y(t)\to t+c_2 \\ \end{align*}