17.3 problem 3

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 }\relax (t )&=-\frac {3 x_{1}\relax (t )}{2}+x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-\frac {x_{1}\relax (t )}{4}-\frac {x_{2}\relax (t )}{2} \end {align*}

Solution by Maple

Time used: 0.02 (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)
 

\[ x_{1}\relax (t ) = 2 \,{\mathrm e}^{-t} \left (c_{2} t +c_{1}-2 c_{2}\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{-t} \left (c_{2} t +c_{1}\right ) \]

Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 52

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} (2 c_2 (t+2)-c_1 t) \\ \end{align*}