72.9.2 problem 2

Internal problem ID [14798]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 07:15:53 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-y\\ y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.099 (sec). Leaf size: 18

dsolve([diff(x(t),t)=2*x(t)-y(t),diff(y(t),t)=0],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 32

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

\begin{align*} x(t)\to \left (c_1-\frac {c_2}{2}\right ) e^{2 t}+\frac {c_2}{2} \\ y(t)\to c_2 \\ \end{align*}