Internal problem ID [10541]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 237
Problem number: 4(e).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )\\ y^{\prime }\left (t \right )&=2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 20
dsolve([diff(x(t),t)=2*x(t)+0*y(t),diff(y(t),t)=0*x(t)+2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{2 t} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 65
DSolve[{x'[t]==2*x[t]+0*y[t],y'[t]==0*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{2 t} \\ y(t)\to c_2 e^{2 t} \\ x(t)\to c_1 e^{2 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*}