Internal problem ID [15527]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 22. Integration of homogeneous
linear systems with constant coefficients. Eulers method. Exercises page 230
Problem number: 804.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve([diff(x(t),t) = 2*x(t)+y(t), diff(y(t),t) = x(t)-3*y(t), x(0) = 0, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= 0 \\ y \left (t \right ) &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 10
DSolve[{x'[t]==2*x[t]+y[t],y'[t]==x[t]-3*y[t]},{x[0]==0,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}