72.15.2 problem 6

Internal problem ID [14883]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 07:18:05 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 16

dsolve([diff(x(t),t)=0*x(t)+0*y(t),diff(y(t),t)=1*x(t)-1*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 27

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

\begin{align*} x(t)\to c_1 \\ y(t)\to e^{-t} \left (c_1 \left (e^t-1\right )+c_2\right ) \\ \end{align*}