Internal problem ID [11534]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 190
Problem number: 2(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=4 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(x(t),t)=4*y(t),diff(y(t),t)=2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= 2 c_{2} {\mathrm e}^{2 t}+c_{1} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 65
DSolve[{x'[t]==4*x[t],y'[t]==2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{4 t} \\ y(t)\to c_2 e^{2 t} \\ x(t)\to c_1 e^{4 t} \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^{2 t} \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}