Internal problem ID [11948]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 7, Systems of linear differential equations. Section 7.4. Exercises page
309
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve([diff(x(t),t)=5*x(t)-2*y(t),diff(y(t),t)=4*x(t)-y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{3 t} \\ y \left (t \right ) &= 2 c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 63
DSolve[{x'[t]==5*x[t]-2*y[t],y'[t]==4*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \left (c_1 \left (2 e^{2 t}-1\right )-c_2 \left (e^{2 t}-1\right )\right ) \\ y(t)\to e^t \left (2 c_1 \left (e^{2 t}-1\right )-c_2 \left (e^{2 t}-2\right )\right ) \\ \end{align*}