Internal problem ID [11951]
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: 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=7 x \left (t \right )+4 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 6, y \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve([diff(x(t),t) = -2*x(t)+y(t), diff(y(t),t) = 7*x(t)+4*y(t), x(0) = 6, y(0) = 2], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{5 t}+5 \,{\mathrm e}^{-3 t} \\ y \left (t \right ) &= 7 \,{\mathrm e}^{5 t}-5 \,{\mathrm e}^{-3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{x'[t]==-2*x[t]+y[t],y'[t]==7*x[t]+4*y[t]},{x[0]==6,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-3 t} \left (e^{8 t}+5\right ) \\ y(t)\to e^{-3 t} \left (7 e^{8 t}-5\right ) \\ \end{align*}