Internal problem ID [11950]
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: 23.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+7 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 9, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve([diff(x(t),t) = -2*x(t)+7*y(t), diff(y(t),t) = 3*x(t)+2*y(t), x(0) = 9, y(0) = -1], singsol=all)
\begin{align*} x \left (t \right ) &= 2 \,{\mathrm e}^{5 t}+7 \,{\mathrm e}^{-5 t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-5 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 38
DSolve[{x'[t]==-2*x[t]+7*y[t],y'[t]==3*x[t]+2*y[t]},{x[0]==9,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 7 e^{-5 t}+2 e^{5 t} \\ y(t)\to 2 e^{5 t}-3 e^{-5 t} \\ \end{align*}