Internal problem ID [768]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-\frac {3 x_{1} \left (t \right )}{2}+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-\frac {x_{1} \left (t \right )}{4}-\frac {x_{2} \left (t \right )}{2} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve([diff(x__1(t),t)=-3/2*x__1(t)+1*x__2(t),diff(x__2(t),t)=-1/4*x__1(t)-1/2*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = 2 \,{\mathrm e}^{-t} \left (c_{2} t +c_{1} -2 c_{2} \right ) \] \[ x_{2} \left (t \right ) = {\mathrm e}^{-t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 54
DSolve[{x1'[t]==-3/2*x1[t]+1*x2[t],x2'[t]==-1/4*x1[t]-1/2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} (2 c_2 t-c_1 (t-2)) \text {x2}(t)\to \frac {1}{4} e^{-t} (c_1 (-t)+2 c_2 t+4 c_2) \end{align*}