Internal problem ID [11778]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 28, Distinct real eigenvalues. Exercises page 282
Problem number: 28.2 (ii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )\\ y^{\prime }\left (t \right )&=-5 x \left (t \right )-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve([diff(x(t),t)=2*x(t),diff(y(t),t)=-5*x(t)-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{2} {\mathrm e}^{2 t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 36
DSolve[{x'[t]==2*x[t],y'[t]==-5*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{2 t} y(t)\to e^{-3 t} \left (c_1 \left (-e^{5 t}\right )+c_1+c_2\right ) \end{align*}