17.9 problem 9

Internal problem ID [774]

Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 9.
ODE order: 1.
ODE degree: 1.

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

With initial conditions \[ [x_{1} \relax (0) = 3, x_{2} \relax (0) = -2] \]

Solution by Maple

Time used: 0.047 (sec). Leaf size: 29

dsolve([diff(x__1(t),t) = 2*x__1(t)+3/2*x__2(t), diff(x__2(t),t) = -3/2*x__1(t)-x__2(t), x__1(0) = 3, x__2(0) = -2],[x__1(t), x__2(t)], singsol=all)
 

\[ x_{1} \relax (t ) = -\frac {{\mathrm e}^{\frac {t}{2}} \left (-\frac {9 t}{2}-9\right )}{3} \] \[ x_{2} \relax (t ) = {\mathrm e}^{\frac {t}{2}} \left (-\frac {3 t}{2}-2\right ) \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 38

DSolve[{x1'[t]==2*x1[t]+3/2*x2[t],x2'[t]==-3/2*x1[t]-1*x2[t]},{x1[0]==3,x2[0]==-2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {3}{2} e^{t/2} (t+2) \\ \text {x2}(t)\to -\frac {1}{2} e^{t/2} (3 t+4) \\ \end{align*}