Internal problem ID [15529]
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: 806.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-5 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
dsolve([diff(x(t),t) = 4*x(t)-5*y(t), diff(y(t),t) = x(t), x(0) = 0, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= -5 \,{\mathrm e}^{2 t} \sin \left (t \right ) \\ y \left (t \right ) &= {\mathrm e}^{2 t} \left (-2 \sin \left (t \right )+\cos \left (t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[{x'[t]==4*x[t]-4*y[t],y'[t]==x[t]},{x[0]==0,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -4 e^{2 t} t \\ y(t)\to e^{2 t} (1-2 t) \\ \end{align*}