Internal problem ID [11763]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 26, Explicit solutions of coupled linear systems. Exercises page 257
Problem number: 26.1 (iii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=6 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve([diff(x(t),t) = 2*x(t)+2*y(t), diff(y(t),t) = 6*x(t)+3*y(t)+exp(t), x(0) = 0, y(0) = 1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {12 \,{\mathrm e}^{6 t}}{35}-\frac {{\mathrm e}^{-t}}{7}-\frac {{\mathrm e}^{t}}{5} \] \[ y \left (t \right ) = \frac {24 \,{\mathrm e}^{6 t}}{35}+\frac {3 \,{\mathrm e}^{-t}}{14}+\frac {{\mathrm e}^{t}}{10} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 58
DSolve[{x'[t]==2*x[t]+2*y[t],y'[t]==6*x[t]+3*y[t]+Exp[t]},{x[0]==0,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{35} e^{-t} \left (-7 e^{2 t}+12 e^{7 t}-5\right ) y(t)\to \frac {1}{70} e^{-t} \left (7 e^{2 t}+48 e^{7 t}+15\right ) \end{align*}