Internal problem ID [12827]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=0\\ y^{\prime }&=x \left (t \right )-y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t)=0*x(t)+0*y(t),diff(y(t),t)=1*x(t)-1*y(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = c_{1} y \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{-t} \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 27
DSolve[{x'[t]==0*x[t]+0*y[t],y'[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*}