Internal problem ID [15550]
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: 827.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-4 y \left (t \right )+1\\ y^{\prime }\left (t \right )&=-x \left (t \right )+5 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve([diff(x(t),t)=2*x(t)-4*y(t)+1,diff(y(t),t)=-x(t)+5*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t}+{\mathrm e}^{6 t} c_{1} -\frac {5}{6} \\ y \left (t \right ) &= \frac {c_{2} {\mathrm e}^{t}}{4}-{\mathrm e}^{6 t} c_{1} -\frac {1}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 67
DSolve[{x'[t]==2*x[t]-4*y[t],y'[t]==-x[t]+5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^t \left (c_1 \left (e^{5 t}+4\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}\right )+4 c_2 e^{5 t}+c_1+c_2\right ) \\ \end{align*}