Internal problem ID [14919]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=x\\ y^{\prime }\left (t \right )&=1 \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
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 \left (t \right ) &= c_{2} +t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 30
DSolve[{x'[t]==x[t],y'[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*}