Internal problem ID [11764]
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 (iv).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{3 t}\\ y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t) = 5*x(t)-4*y(t)+exp(3*t), diff(y(t),t) = x(t)+y(t), x(0) = 1, y(0) = -1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{3 t} \left (t^{2}+7 t +1\right ) \] \[ y \left (t \right ) = \frac {{\mathrm e}^{3 t} \left (t^{2}+6 t -2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 39
DSolve[{x'[t]==5*x[t]-4*y[t]+Exp[3*t],y'[t]==x[t]+y[t]},{x[0]==1,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{3 t} \left (t^2+7 t+1\right ) y(t)\to \frac {1}{2} e^{3 t} \left (t^2+6 t-2\right ) \end{align*}