70.1.13 problem 2.2 (vii)

Internal problem ID [14303]
Book : Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999. Oxford Univ. Press. NY
Section : Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number : 2.2 (vii)
Date solved : Tuesday, January 28, 2025 at 06:26:01 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=0\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 13

dsolve([diff(x(t),t)=0,diff(y(t),t)=x(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 17

DSolve[{D[x[t],t]==0,D[y[t],t]==x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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