Internal problem ID [11554]
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(f).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-6 y \left (t \right )\\ y^{\prime }\left (t \right )&=6 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 23
dsolve([diff(x(t),t)=-6*y(t),diff(y(t),t)=6*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{2} {\mathrm e}^{6 t}+c_{1} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 30
DSolve[{x'[t]==-6*y[t],y'[t]==6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -c_2 e^{6 t}+c_1+c_2 y(t)\to c_2 e^{6 t} \end{align*}