Internal problem ID [11765]
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 (v).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+5 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+4 \cos \left (t \right )^{3}-3 \cos \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 66
dsolve([diff(x(t),t) = 2*x(t)+5*y(t), diff(y(t),t) = -2*x(t)+cos(3*t), x(0) = 2, y(0) = -1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {16 \,{\mathrm e}^{t} \sin \left (3 t \right )}{111}+\frac {69 \,{\mathrm e}^{t} \cos \left (3 t \right )}{37}-\frac {30 \sin \left (3 t \right )}{37}+\frac {5 \cos \left (3 t \right )}{37} \] \[ y \left (t \right ) = -\frac {121 \,{\mathrm e}^{t} \sin \left (3 t \right )}{111}-\frac {17 \,{\mathrm e}^{t} \cos \left (3 t \right )}{37}-\frac {20 \cos \left (3 t \right )}{37}+\frac {9 \sin \left (3 t \right )}{37} \]
✓ Solution by Mathematica
Time used: 0.363 (sec). Leaf size: 70
DSolve[{x'[t]==2*x[t]+5*y[t],y'[t]==-2*x[t]+Cos[3*t]},{x[0]==2,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{111} \left (3 \left (69 e^t+5\right ) \cos (3 t)-2 \left (8 e^t+45\right ) \sin (3 t)\right ) y(t)\to \frac {1}{111} \left (-\left (121 e^t-27\right ) \sin (3 t)-3 \left (17 e^t+20\right ) \cos (3 t)\right ) \end{align*}