Internal problem ID [11945]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 30
dsolve([diff(x(t),t) = 3*x(t)+4*y(t), diff(y(t),t) = 2*x(t)+y(t), x(0) = 1, y(0) = 2], singsol=all)
\begin{align*} x \left (t \right ) &= 2 \,{\mathrm e}^{5 t}-{\mathrm e}^{-t} \\ y \left (t \right ) &= {\mathrm e}^{5 t}+{\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 34
DSolve[{x'[t]==3*x[t]+4*y[t],y'[t]==2*x[t]+y[t]},{x[0]==1,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} \left (2 e^{6 t}-1\right ) \\ y(t)\to e^{-t}+e^{5 t} \\ \end{align*}