Internal problem ID [11946]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 7, Systems of linear differential equations. Section 7.3. Exercises page
299
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )+y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 8] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = 5*x(t)+3*y(t), diff(y(t),t) = 4*x(t)+y(t), x(0) = 0, y(0) = 8], singsol=all)
\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{7 t}-3 \,{\mathrm e}^{-t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{7 t}+6 \,{\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 36
DSolve[{x'[t]==5*x[t]+3*y[t],y'[t]==4*x[t]+y[t]},{x[0]==0,y[0]==8},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 e^{-t} \left (e^{8 t}-1\right ) \\ y(t)\to 2 e^{-t} \left (e^{8 t}+3\right ) \\ \end{align*}