Internal problem ID [11780]
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 (iv).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+20 y \left (t \right )\\ y^{\prime }\left (t \right )&=40 x \left (t \right )-19 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve([diff(x(t),t)=x(t)+20*y(t),diff(y(t),t)=40*x(t)-19*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{21 t}-\frac {c_{2} {\mathrm e}^{-39 t}}{2} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{21 t}+c_{2} {\mathrm e}^{-39 t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 71
DSolve[{x'[t]==x[t]+20*y[t],y'[t]==40*x[t]-19*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-39 t} \left (c_1 \left (2 e^{60 t}+1\right )+c_2 \left (e^{60 t}-1\right )\right ) y(t)\to \frac {1}{3} e^{-39 t} \left (2 c_1 \left (e^{60 t}-1\right )+c_2 \left (e^{60 t}+2\right )\right ) \end{align*}