63.19.3 problem 1(c)

Internal problem ID [13217]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 202
Problem number : 1(c)
Date solved : Tuesday, January 28, 2025 at 05:12:34 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 35

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

\begin{align*} x(t)\to c_1 e^{-2 t} \\ y(t)\to c_1 \left (\frac {1}{2}-\frac {e^{-2 t}}{2}\right )+c_2 \\ \end{align*}