Internal problem ID [750]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.5, Homogeneous Linear Systems with Constant Coefficients. page 407
Problem number: 30.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-\frac {x_{1} \relax (t )}{10}+\frac {3 x_{2} \relax (t )}{40}\\ x_{2}^{\prime }\relax (t )&=\frac {x_{1} \relax (t )}{10}-\frac {x_{2} \relax (t )}{5} \end {align*}
With initial conditions \[ [x_{1} \relax (0) = -17, x_{2} \relax (0) = -21] \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = -1/10*x__1(t)+3/40*x__2(t), diff(x__2(t),t) = 1/10*x__1(t)-1/5*x__2(t), x__1(0) = -17, x__2(0) = -21],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {29 \,{\mathrm e}^{-\frac {t}{4}}}{8}-\frac {165 \,{\mathrm e}^{-\frac {t}{20}}}{8} \] \[ x_{2} \relax (t ) = -\frac {29 \,{\mathrm e}^{-\frac {t}{4}}}{4}-\frac {55 \,{\mathrm e}^{-\frac {t}{20}}}{4} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 52
DSolve[{x1'[t]==-1/10*x1[t]+3/40*x2[t],x2'[t]==1/10*x1[t]-1/5*x2[t]},{x1[0]==-17,x2[0]==-21},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{8} e^{-t/4} \left (29-165 e^{t/5}\right ) \\ \text {x2}(t)\to -\frac {1}{4} e^{-t/4} \left (55 e^{t/5}+29\right ) \\ \end{align*}