Internal problem ID [15548]
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 23.3 dAlemberts method. Exercises
page 243
Problem number: 825.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{6 t} \\ y \left (t \right ) &= -c_{1} {\mathrm e}^{t}+\frac {c_{2} {\mathrm e}^{6 t}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 67
DSolve[{x'[t]==5*x[t]+4*y[t],y'[t]==x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^t \left (c_1 \left (4 e^{5 t}+1\right )+4 c_2 \left (e^{5 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^t \left (c_1 \left (e^{5 t}-1\right )+c_2 \left (e^{5 t}+4\right )\right ) \\ \end{align*}