Internal problem ID [15528]
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: 805.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=4 y \left (t \right )-2 x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve([diff(x(t),t) = x(t)+y(t), diff(y(t),t) = 4*y(t)-2*x(t), x(0) = 0, y(0) = -1], singsol=all)
\begin{align*} x \left (t \right ) &= -{\mathrm e}^{3 t}+{\mathrm e}^{2 t} \\ y \left (t \right ) &= -2 \,{\mathrm e}^{3 t}+{\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 33
DSolve[{x'[t]==x[t]+y[t],y'[t]==4*y[t]-2*x[t]},{x[0]==0,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{2 t} \left (e^t-1\right ) \\ y(t)\to e^{2 t}-2 e^{3 t} \\ \end{align*}